{ "paper_id": "J91-2003", "header": { "generated_with": "S2ORC 1.0.0", "date_generated": "2023-01-19T02:15:03.668681Z" }, "title": "Semantics of Paragraphs", "authors": [ { "first": "Wlodek", "middle": [], "last": "Zadrozny", "suffix": "", "affiliation": {}, "email": "" }, { "first": "Karen", "middle": [], "last": "Jensew", "suffix": "", "affiliation": {}, "email": "" }, { "first": "Ibm", "middle": [ "T J" ], "last": "Watson", "suffix": "", "affiliation": {}, "email": "" }, { "first": "Research", "middle": [], "last": "Center", "suffix": "", "affiliation": {}, "email": "" } ], "year": "", "venue": null, "identifiers": {}, "abstract": "We present a computational theory of the paragraph. Within it we formally define coherence, give semantics to the adversative conjunction \"but\" and to the Gricean maxim of quantity, and present some new methods for anaphora resolution. The theory precisely characterizes the relationship between the content of the paragraph and background knowledge needed for its understanding. This is achieved by introducing a new type of logical theory consisting of an object level, corresponding to the content of the paragraph, a referential level, which is a new logical level encoding background knowledge, and a metalevel containing constraints on models of discourse (e.g. a formal version of Gricean maxims). We propose also specific mechanisms of interaction between these levels, resembling both classical provability and abduction. Paragraphs are then represented by a class of structures called p-models.", "pdf_parse": { "paper_id": "J91-2003", "_pdf_hash": "", "abstract": [ { "text": "We present a computational theory of the paragraph. Within it we formally define coherence, give semantics to the adversative conjunction \"but\" and to the Gricean maxim of quantity, and present some new methods for anaphora resolution. The theory precisely characterizes the relationship between the content of the paragraph and background knowledge needed for its understanding. This is achieved by introducing a new type of logical theory consisting of an object level, corresponding to the content of the paragraph, a referential level, which is a new logical level encoding background knowledge, and a metalevel containing constraints on models of discourse (e.g. a formal version of Gricean maxims). We propose also specific mechanisms of interaction between these levels, resembling both classical provability and abduction. Paragraphs are then represented by a class of structures called p-models.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Abstract", "sec_num": null } ], "body_text": [ { "text": "Logic and knowledge have been often discussed by linguists. Anaphora is another prominent subject in linguistic analyses. Not so frequently examined are different types of cohesion. And it is quite rare to find the word \"paragraph\" in articles or books about natural language understanding, although paragraphs are grammatical units and units of discourse. But it is possible to speak formally about the role of background knowledge, cohesion, coherence and anaphora--all within one, flexible and natural, logical system--if one examines the semantic role of the linguistic construct called a paragraph.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1." }, { "text": "Paragraphs have been sometimes described, rather loosely, as \"units of thought.\" We establish a correspondence between them and certain types of logical models, thereby making the characterization of paragraphs more precise. The correspondence gives us also an opportunity to identify and attack--with some success, we believe-three interesting and important problems: (1) how to define formally coherence and topic, (2) how to resolve anaphora, and 3what is the formal meaning of linkages (connectives) such as but, however, and, certainly, usually, because, then, etc . These questions are central from our point of view because: (1) the \"unity\" of a paragraph stems from its coherence, while the \"aboutness\" of thought can be, at least to some extent, described as existence of a topic; (2) without determining reference of pronouns and phrases, the universes of the models are undefined; and (3) the linkages, which make sentences into paragraphs, have semantic roles that must be accounted for. We can explain then the process of building a computational model of a paragraph (a p-model) as an interaction between its sentences, background knowledge to which these sentences refer, and metatheoretical operators that indicate types of permitted models.", "cite_spans": [ { "start": 517, "end": 569, "text": "however, and, certainly, usually, because, then, etc", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1." }, { "text": "At this point the reader may ask: what is so special about paragraphs; does all this mean that a chapter, a book or a letter do not have any formal counterparts? We believe they do. But we simply do not yet know how corresponding formal structures would be created from models of paragraphs. ~Ib answer this question we may need more advanced theories of categorization and learning than exist today. On the other hand, the paragraph is the right place to begin: it is the next grammatical unit after the sentence; connectives providing cohesion operate here, not at the level of an entire discourse; and it is the smallest reasonable domain of anaphora resolution. Furthermore, we will argue, it is the smallest domain in which topic and coherence can be defined.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1." }, { "text": "The formalization of paragraph structure requires the introduction of a new type of logical theory and a corresponding class of models. As we know, the usual logical structures consist of an object level theory T and provability relation F-; within the context of the semantics of natural language, the object theory contains a logical translation of the surface form of sentences, and F-is the standard provability relation (logical consequence). In mathematical logic, this scheme is sometimes extended by adding a metalevel assumption, for instance postulating the standardness of natural numbers. In artificial intelligence, a metarule typically, the closed world assumption of circumscription---can be used in dealing with theoretical questions, like the frame problem. But a formal account of natural language understanding requires more. It requires at least a description (a) of how background knowledge about objects and relations that the sentences describe is used in the process of understanding, and (b) of general constraints on linguistic communications, as expressed for instance in Gricean maxims. It is well known that without the former it is impossible to find references of pronouns or attachments of prepositional phrases; background knowledge, as it turns out, is also indispensable in establishing coherence. We have then reasons for introducing a new logical level--a referential level R, which codes the background knowledge.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1." }, { "text": "As for Gricean maxims, we show that they can be expressed formally and can be used in a computational model of communication. We include them in a metalevel M, which contains global constraints on models of a text and definitions of meta-operators such as the conjunction but. We end up with three-level logical theories (M, T, R, ~-R + M), where a provability relation ~-~ + M, based on R and M, can be used, for example, to establish the reference of pronouns.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1." }, { "text": "This work is addressed primarily to our colleagues working on computational models of natural language; but it should be also of interest to linguists, logicians, and philosophers. It should be of interest to linguists because the notion that a paragraph is equivalent to a model is something concrete to discuss; because p-models are as formal as formal languages (and therefore something satisfyingly theoretical to argue about); and because new directions for analysis are opened beyond the sentence. The work should be of interest to logicians because it introduces a new type of three-level theory, and corresponding models. The theory of these structures, which are based on linguistic constructs, will differ from classical model theory--for instance, by the fact that names of predicates of an object theory matter, because they connect the object theory with the referential level. This work should be of interest to philosophers for many of the same reasons: it makes more sense to talk about the meaning of a paragraph than about the meaning of a sentence. The following parallel can be drawn: a sentence is meaningful only with respect to a model of a paragraph, exactly as the truth value of a formula can be computed only with respect to a given model. Moreover, it is possible in this framework to talk about meaning without mentioning the idea of possible worlds. However, we do not identify meaning with truth conditions; in this paper, the meaning of a sentence is its role in the model of the paragraph in which this sentence occurs. Our intuitive concept of meaning is similar to Lakoff's (1987) Idealized Cognitive Model (ICM). Needless to say, we believe in the possibility of formalizing ICMs, although in this paper we will not try to express, in logic, prototype effects, metaphors, or formal links with vision.", "cite_spans": [ { "start": 1600, "end": 1615, "text": "Lakoff's (1987)", "ref_id": "BIBREF41" } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1." }, { "text": "The paper is presented in six sections. In Section 2, we discuss the grammatical function of the paragraph and we show, informally, how a formal model of a paragraph might actually be built. In Section 3 we give the logical preliminaries to our analysis. We discuss a three-part logical structure that includes a referential level, and we introduce a model for plausible meaning. Section 4 discusses paragraph coherence, and Section 5 constructs a model of a paragraph, a p-model, based on the information contained in the paragraph itself and background information contained in the referential level R. Section 5 further motivates the use of the referential level, showing how it contributes to the resolution of anaphoric reference. In Section 6, we broaden our presentation of the metalevel, introducing some metalevel axioms, and sketching ways by which they can be used to reduce ambiguity and construct new models. We also show metalevel rules for interpreting \"but.\"", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1." }, { "text": "its segments are distinguished by bearing distinct relationships to the paragraph topic (which is central, but nowhere clearly defined). Segments themselves are composed of clauses and regulated by \"switching\" patterns, such as the question-answer pattern and the remark-reply pattern.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Approaches to Paragraph Analysis", "sec_num": "2.1" }, { "text": "Although there are other discussions of the paragraph as a central element of discourse (e.g. Chafe 1979 , Halliday and Hasan 1976 , Longacre 1979 , Haberlandt et al. 1980 , all of them share a certain limitation in their formal techniques for analyzing paragraph structure. Discourse linguists show little interest in making the structural descriptions precise enough so that a computational grammar of text could adapt them and use them. Our interest, however, lies precisely in that area.", "cite_spans": [ { "start": 94, "end": 104, "text": "Chafe 1979", "ref_id": "BIBREF6" }, { "start": 105, "end": 130, "text": ", Halliday and Hasan 1976", "ref_id": null }, { "start": 131, "end": 146, "text": ", Longacre 1979", "ref_id": "BIBREF43" }, { "start": 147, "end": 171, "text": ", Haberlandt et al. 1980", "ref_id": "BIBREF20" } ], "ref_spans": [], "eq_spans": [], "section": "Our View of Paragraphs: An Informal Sketch", "sec_num": "2.2" }, { "text": "We suggest that the paragraph is a grammatical and logical unit. It is the smallest linguistic representation of what, in logic, is called a \"model,\" and it is the first reasonable domain of anaphora resolution, and of coherent thought about a central topic.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Our View of Paragraphs: An Informal Sketch", "sec_num": "2.2" }, { "text": "A paragraph can be thought of as a grammatical unit in the following sense: it is the discourse unit in which a functional (or a predicate-argument) structure can be definitely assigned to sentences/strings. For instance, Sells (1985, p. 8) says that the sentence \"Reagan thinks bananas,\" which is otherwise strange, is in fact acceptable if it occurs as an answer to the question \"What is Kissinger's favorite fruit?\" The pairing of these two sentences may be said to create a small paragraph. Our point is that an acceptable structure can be assigned to the utterance \"Reagan thinks bananas\" only within the paragraph in which this utterance occurs. We believe that, in general, no unit larger than a paragraph is necessary to assign a functional structure to a sentence, and that no smaller discourse fragment, such as two (or one) neighboring sentences, will be sufficient for this task. That is, we can ask in the first sentence of a paragraph about Kissinger's favorite fruit, elaborate the question and the circumstances in the next few sentences, and give the above answer at the end. We do not claim that a paragraph is necessarily described by a set of grammar rules in some grammar formalism (although it may be); rather, it has the grammatical role of providing functional structures that can be assigned to strings.", "cite_spans": [ { "start": 222, "end": 240, "text": "Sells (1985, p. 8)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Our View of Paragraphs: An Informal Sketch", "sec_num": "2.2" }, { "text": "The logical structure of paragraphs will be analyzed in the next sections. At this point we would like to present some intuitions that led to this analysis. But first we want to identify our point of departure. In order to resolve anaphora and to establish the coherence or incoherence of a text, one must appeal to the necessary background knowledge. Hence, a formal analysis of paragraphs must include a formal description of background knowledge and its usage. Furthermore, this background knowledge cannot be treated as a collection of facts or formulas in some formal language, because that would preclude dealing with contradictory word senses, or multiple meanings. Secondly, this background knowledge is not infinite and esoteric. In fact, to a large extent it can be found in standard reference works such as dictionaries and encyclopedias.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Our View of Paragraphs: An Informal Sketch", "sec_num": "2.2" }, { "text": "To argue for these points, we can consider the following paragraph: 1", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Our View of Paragraphs: An Informal Sketch", "sec_num": "2.2" }, { "text": "In the summer of 1347 a merchant ship returning from the Black Sea entered the Sicilian port of Messina bringing with it the horrifying disease that came to be known as the Black Death. It struck rapidly. Within twenty-four hours of infection and the appearance of the first small black pustule came an agonizing death. The effect of the Black Death was appalling. In less than twenty years half the population of Europe had been killed, the countryside devastated, and a period of optimism and growing economic welfare had been brought to a sudden and catastrophic end.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Our View of Paragraphs: An Informal Sketch", "sec_num": "2.2" }, { "text": "The sentences that compose a paragraph must stick together; to put it more technically, they must cohere. This means very often that they show cohesion in the sense of Halliday (1976) --semantic links between elements. Crucially, also, the sentences of a paragraph must all be related to a topic.", "cite_spans": [ { "start": 168, "end": 183, "text": "Halliday (1976)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Our View of Paragraphs: An Informal Sketch", "sec_num": "2.2" }, { "text": "However, in the example paragraph, very few instances can be found here of the formal grammatical devices for paragraph cohesion. There are no connectives, and there are only two anaphoric pronouns (both occurrences of \"it'0. In each case, there are multiple possible referents for the pronoun. The paragraph is coherent because it has a topic: \"Black Death\"; all sentences mention it, explicitly or implicitly.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Our View of Paragraphs: An Informal Sketch", "sec_num": "2.2" }, { "text": "Notice that resolving anaphora precedes the discovery of a topic. A few words about this will illustrate the usage of background knowledge. By parsing with syntactic information alone, we show that resolution of the first \"it\" reference hinges on the proper attachment of the participial clause \"bringing within it... \". If the \"bringing\" clause modifies \"Messina,\" then \"Messina\" is the subject of '`bringing\" and must be the referent for \"it.\" If the clause modifies \"port,\" then \"port\" is the desired referent; if the clause is attached at the level of the main verb of the sentence, then \"ship\" is the referent.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Our View of Paragraphs: An Informal Sketch", "sec_num": "2.2" }, { "text": "But syntactic relations do not suffice to resolve anaphora: Hobbs' (1976) algorithm for resolving the reference of pronouns, depending only on the surface syntax of sentences in the text, when applied to \"it\" in the example paragraph, fails in both cases to identify the most likely referent NP.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Our View of Paragraphs: An Informal Sketch", "sec_num": "2.2" }, { "text": "Adding selectional restrictions (semantic feature information, Hobbs 1977) does not solve the problem, because isolated features offer only part of the background knowledge necessary for reference disambiguation. Later, Hobbs (1979 Hobbs ( , 1982 proposed a knowledge base in which information about language and the world would be encoded, and he emphasized the need for using \"salience\" in choosing facts from this knowledge base.", "cite_spans": [ { "start": 220, "end": 231, "text": "Hobbs (1979", "ref_id": "BIBREF28" }, { "start": 232, "end": 246, "text": "Hobbs ( , 1982", "ref_id": "BIBREF27" } ], "ref_spans": [], "eq_spans": [], "section": "Our View of Paragraphs: An Informal Sketch", "sec_num": "2.2" }, { "text": "We will investigate the possibility that the structure of this knowledge base can actually resemble the structure of, for example, natural language dictionaries. The process of finding referents could then be automated.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Our View of Paragraphs: An Informal Sketch", "sec_num": "2.2" }, { "text": "Determining that the most likely subject for \"bringing,\" in the first sentence, is the noun \"ship\" is done in the following fashion. The first definition for \"bring\" in W7 (Webster's Seventh Collegiate Dictionary) is \"to convey, lead, carry, or cause to come along with one...\" The available possible subjects for \"bringing\" are \"Messina,\" \"port,\" and \"ship.\" \"Messina\" is listed in the Pronouncing Gazetteer of W7, which means that it is a place (and is so identified in the subtitle of the Gazetteer). So we can substitute the word \"place\" for the word \"Messina.\" Then we check the given definitions for the words \"place,\" \"port,\" and \"ship\" in both dictionaries. LDOCE (Longman Dictionary of Contemporary English) proves particularly useful at this point. Definitions for \"place\" begin: \"a particular part of space... \". Definitions for \"port\" include: \"harbour... \"; \"an opening in the side of a ship... \". But the first entry for \"ship\" in LDOCE reads \"a large boat for carrying people or goods... \". This demonstrates a very quick connection with the definition for the verb \"bring,\" since the word \"carry\" occurs in both definitions. It requires much more time and effort to find a connection between \"bring\" and either of the other two candidate subject words \"place\" or \"port.\" Similar techniques can be used to assign \"disease\" as the most probable referent for the second \"it\" anaphor in our example paragraph. Equally significant in this instance is the realization that a dictionary points to synonym and paraphrase relations, and thereby verifies the cohesiveness of the passage. Through the dictionary (LDOCE again), we establish shared-word relationships between and among the words \"disease,\" \"Black death,\" \"infection,\" \"death,\" \"killed,\" and \"end.\" Note that there is no other means, short of appealing to human understanding or to some hand-coded body of predicate assertions, for making these relationships.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Our View of Paragraphs: An Informal Sketch", "sec_num": "2.2" }, { "text": "This demonstrates that information needed to identify and resolve anaphoric references can be found, to an interesting extent, in standard dictionaries and thesauri. (Other reference works could be treated as additional sources of world knowledge.) This type of consultation uses existing natural language texts as a referential level for processing purposes. It is the lack of exactly this notion of referential level that has stood in the way of other linguists who have been interested in the paragraph as a unit. Crothers (1979, p. 112) , for example, bemoans the fact that his \"theory lacks a world knowledge component, a mental 'encyclopedia,' which could be invoked to generate inferences... \". With respect to that independent source of knowledge, our main contributions are two. First, we identify its possible structure (a collection of partially ordered theories) and make formal the choice of a most plausible interpretation. In other words, we recognize it as a separate logical level--the referential level. Second, we suggest that natural language reference works, like dictionaries and thesauri, can quite often fill the role of the referential level.", "cite_spans": [ { "start": 517, "end": 540, "text": "Crothers (1979, p. 112)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Our View of Paragraphs: An Informal Sketch", "sec_num": "2.2" }, { "text": "The goal of this section is to introduce a formalism describing how background knowledge is used in understanding text. The term \"logic of reference\" denotes a formal description of this process of consulting various sources of information in order to produce an interpretation of a text. The formalist will be presented in a number of steps in which we will elaborate one simple example:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The Logic of Reference", "sec_num": "3." }, { "text": "Entering the port, a ship brought a disease.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Example 1", "sec_num": null }, { "text": "This sentence can be translated into the logical formula (ignoring only the past tense of \"bring\" and the progressive of \"enter'9:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Example 1", "sec_num": null }, { "text": "Definition S: enter(xl~ x2) & ship(x1) & port(x2) & bring(x3~ x4) & disease(x4) & xl = s & x2 = m & x3 = s & x4 = d, where s, m, d, are constants.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Example 1", "sec_num": null }, { "text": "We adopt the three-level semantics as a formal tool for the analysis of paragraphs. This semantics was constructed (Zadrozny 1987a (Zadrozny , 1987b ) as a formal framework for default and commonsense reasoning. It should not come as a surprise that we can now use this apparatus for text/discourse analysis; after all, many natural language inferences are based on defaults, and quite often they can be reduced to choosing most plausible interpretations of predicates. For instance, relating \"they\" to \"apples\" in the sentence (cf. Haugeland 1985 p. 195; Zadrozny 1987a) :", "cite_spans": [ { "start": 115, "end": 130, "text": "(Zadrozny 1987a", "ref_id": "BIBREF68" }, { "start": 131, "end": 148, "text": "(Zadrozny , 1987b", "ref_id": "BIBREF69" }, { "start": 533, "end": 555, "text": "Haugeland 1985 p. 195;", "ref_id": null }, { "start": 556, "end": 571, "text": "Zadrozny 1987a)", "ref_id": "BIBREF68" } ], "ref_spans": [], "eq_spans": [], "section": "Example 1", "sec_num": null }, { "text": "We bought the boys apples because they were so cheap can be an example of such a most plausible choice.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Example 1", "sec_num": null }, { "text": "The main ideas of the three-level semantics can be stated as follows:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Example 1", "sec_num": null }, { "text": "1. Reasoning takes place in a three-level structure consisting of an object level, a referential level, and a metalevel.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Example 1", "sec_num": null }, { "text": "2. The object level is used to describe the current situation, and in our case is reserved for the formal representation of paragraph sentences. For the sake of simplicity, the object level will consist of a first order theory.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Example 1", "sec_num": null }, { "text": "3. The referential level, denoted by R, consists of theories representing background knowledge, from which information relevant to the understanding of a given piece of text has to be extracted. It constrains interpretations of the predicates of an object theory. Its structure and the extraction methods will be discussed below.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Example 1", "sec_num": null }, { "text": "4. Understanding has as its goal construction of an interpretation of the text, i.e. building some kind of model. Since not all logically permissible models are linguistically appropriate, one needs a place, namely the metalevel, to put constraints on types of models. Gricean maxims belong there; Section 6 will be devoted to a presentation of the metalevel rules corresponding to them.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Example 1", "sec_num": null }, { "text": "We have shown elsewhere (Jensen and Binot 1988; Zadrozny 1987a Zadrozny , 1987b ) that natural language programs, such as on-line grammars and dictionaries, can be used as referential levels for commonsense reasoning--for example, to disambiguate PP attachment. This means that information contained in grammars and dictionaries can be used to constrain possible interpretations of the logical predicates of an object-level theory.", "cite_spans": [ { "start": 24, "end": 47, "text": "(Jensen and Binot 1988;", "ref_id": "BIBREF36" }, { "start": 48, "end": 62, "text": "Zadrozny 1987a", "ref_id": "BIBREF68" }, { "start": 63, "end": 79, "text": "Zadrozny , 1987b", "ref_id": "BIBREF69" } ], "ref_spans": [], "eq_spans": [], "section": "Example 1", "sec_num": null }, { "text": "The referential structures we are going to use are collections of logical theories, but the concept of reference is more general. Some of the intuitions we associate with this notion have been very well expressed by Turner (1987, pp. 7-8): ... Semantics is constrained by our models of ourselves and our worlds. We have models of up and down that are based by the way our bodies actually function.", "cite_spans": [ { "start": 216, "end": 239, "text": "Turner (1987, pp. 7-8):", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Example 1", "sec_num": null }, { "text": "Once the word \"up\" is given its meaning relative to our experience with gravity, it is not free to \"slip\" into its opposite. \"Up\" means up and not down .... We have a model that men and women couple to produce offspring who are similar to their parents, and this model is grounded in genetics, and the semantics of kinship metaphor is grounded in this model. Mothers have a different role than fathers in this model, and thus there is a reason why \"Death is the father of beauty\" fails poetically while \"Death is the mother of beauty\" succeeds .... It is precisely this \"grounding\" of logical predicates in other conceptual structures that we would like to capture. We investigate here only the \"grounding\" in logical theories. However, it is possible to think about constraining linguistic or logical predicates by simulating physical experiences (cf. Woods 1987) .", "cite_spans": [ { "start": 853, "end": 864, "text": "Woods 1987)", "ref_id": "BIBREF67" } ], "ref_spans": [], "eq_spans": [], "section": "Example 1", "sec_num": null }, { "text": "We assume here that a translation of the surface forms of sentences into a logical formalism is possible. Its details are not important for our aim of giving a semantic interpretation of paragraphs; the main theses of our theory do not depend on a logical notation. So we will use a very simple formalism, like the one above, resembling the standard first order language. But, obviously, there are other possibilities--for instance, the discourse representation structures (DRS's) of Kamp (1981) , which have been used to translate a subset of English into logical formulas, to model text (identified with a list of sentences), to analyze a fragment of English, and to deal with anaphora. The logical notation of Montague (1970) is more sophisticated, and may be considered another possibility. Jackendoff's (1983) formalism is richer and resembles more closely an English grammar. Jackendoff (1983, p. 14) writes \"it would be perverse not to take as a working assumption that language is a relatively efficient and accurate encoding of the information it conveys.\" Therefore a formalism of the kind he advocates would probably be most suitable for an implementation of our semantics. It will also be a model for our simplified logical notation (cf. Section 5). We can envision a system that uses data structures produced by a computational grammar to obtain the logical form of sentences.", "cite_spans": [ { "start": 484, "end": 495, "text": "Kamp (1981)", "ref_id": "BIBREF38" }, { "start": 713, "end": 728, "text": "Montague (1970)", "ref_id": "BIBREF48" }, { "start": 795, "end": 814, "text": "Jackendoff's (1983)", "ref_id": "BIBREF33" }, { "start": 882, "end": 906, "text": "Jackendoff (1983, p. 14)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Example 1", "sec_num": null }, { "text": "Unless explicitly stated otherwise, we assume that formulas are expressed in a certain (formal) language L without equality; the extension L(=) of L is going to be used only in Section 5 for dealing with noun phrase references. This means that natural language expressions such as \"A is B,\" \"A is the same as B,\" etc. are not directly represented by logical equality; similarly, \"not\" is often not treated as logical negation; cf. Hintikka (1985) .", "cite_spans": [ { "start": 431, "end": 446, "text": "Hintikka (1985)", "ref_id": "BIBREF24" } ], "ref_spans": [], "eq_spans": [], "section": "Finite Representations, Finite Theories", "sec_num": "3.1" }, { "text": "All logical notions that we are going to consider, such as theory or model, will be finitary. For example, a model would typically contain fewer than a hundred elements of different logical sorts. Therefore these notions, and all other constructs we are going to define (axioms, metarules, definitions etc.) are computational, although usually we will not provide explicit algorithms for computing them. The issues of control are not so important for us at this point; we restrict ourselves to describing the logic. This Principle of Finitism is also assumed by Johnson-Laird (1983 ), Jackendoff (1983 , Kamp (1981) , and implicitly or explicitly by almost all researchers in computational linguistics. As a logical postulate it is not very radical; it is possible within a finitary framework to develop that part of mathematics that is used or has potential applications in natural science, such as mathematical analysis (cf. Mycielski 1981) .", "cite_spans": [ { "start": 562, "end": 581, "text": "Johnson-Laird (1983", "ref_id": "BIBREF37" }, { "start": 582, "end": 601, "text": "), Jackendoff (1983", "ref_id": "BIBREF33" }, { "start": 604, "end": 615, "text": "Kamp (1981)", "ref_id": "BIBREF38" }, { "start": 927, "end": 942, "text": "Mycielski 1981)", "ref_id": "BIBREF49" } ], "ref_spans": [], "eq_spans": [], "section": "Finite Representations, Finite Theories", "sec_num": "3.1" }, { "text": "On the other hand, a possible obstacle to our strategy of using only finite objects is the fact that the deductive closure of any set of formulas is not finite in standard logic, while, clearly, we will have to deduce new facts from formal representations of text and background knowledge. But there are several ways to avoid this obstruction. For example, consider theories consisting of universal formulas without function symbols.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Finite Representations, Finite Theories", "sec_num": "3.1" }, { "text": "Let Th(T) of such a theory T be defined as T plus ground clauses/sets of literals provable from T in standard logic. It is easily seen that it is a closure, i.e. Th(Th(T)) = Th(T); and obviously, it is finite, for finite T. It makes sense then to require that logical consequences of paragraph sentences have similar finite representations. However, in order not to limit the expressive power of the formal language, we should proceed in a slightly different manner. The easiest way to achieve the above requirement is by postulating that all universes of discourse are always finite, and therefore all quantifiers actually range over finite domains. In practice, we would use those two and other tricks: we could forbid more than three quantifier changes, because even in mathematics more than three are rare; we could restrict the size of universes of discourse to some large number such as 1001; we could allow only a fixed finite nesting of function symbols (or operators) in formulas; etc. The intention of this illustration was to convince the reader that we now can introduce the following set of definitions.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Finite Representations, Finite Theories", "sec_num": "3.1" }, { "text": "\u2022 A theory is a finite set of sentences Sent (formulas without free variables in some formal language).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Definitions", "sec_num": null }, { "text": "\u2022 A deductive closure operator is a function Th : P(Sent) --* P(Sent) (a) T c Th(T), for any T, (b) Th(Th(T)) = Th(T), (c) Th(T) is finite, for finite T; additionally, we require it to be ground, for ground T.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Definitions", "sec_num": null }, { "text": "\u2022 A theory T is consistent if there is no formula ~ such that both ~ and -~ belong to Th(T) (and inconsistent otherwise).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Definitions", "sec_num": null }, { "text": "\u2022 A model of a theory T is defined, as usual, as an interpretation defined on a certain domain, which satisfies all formulas of T. The collection of all (finite) models of a theory T will be denoted by Mods(T).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Definitions", "sec_num": null }, { "text": "\u2022 The set of all subformulas of a collection of formulas F is denoted by Form(F). ~ is a ground instance of a formula G if ~ contains no variables, and ~ = ~, for some substitution 0.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Definitions", "sec_num": null }, { "text": "Thus, we do not require Th(T) to be closed under substitution instances of tautologies. Although in this paper we take modus ponens as the main rule of inference, in general one can consider deductive closures with respect to weaker, nonstandard logics, (cf. Levesque 1984; Frisch 1987; Patel-Schneider 1985) . But we won't pursue this topic further here.", "cite_spans": [ { "start": 259, "end": 273, "text": "Levesque 1984;", "ref_id": "BIBREF42" }, { "start": 274, "end": 286, "text": "Frisch 1987;", "ref_id": "BIBREF10" }, { "start": 287, "end": 308, "text": "Patel-Schneider 1985)", "ref_id": "BIBREF50" } ], "ref_spans": [], "eq_spans": [], "section": "Definitions", "sec_num": null }, { "text": "Background knowledge is not a simple list of meaning postulates--it has a structure and it may contain contradictions and ambiguities. These actualities have to be taken into account in any realistic model of natural language understanding. For instance, the verb \"enter\" is polysemous. But, unless context specifies otherwise, \"to come in\" is a more plausible meaning than \"to join a group.\" Assuming some logical representation of this knowledge, we can write that", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The Structure of Background Knowledge", "sec_num": "3.2" }, { "text": "EQUATION", "cite_spans": [], "ref_spans": [], "eq_spans": [ { "start": 0, "end": 8, "text": "EQUATION", "ref_id": "EQREF", "raw_str": "enter(x, y) --* {come_in (x~ y); place(y)} enter(x, y) --* {join(x, y)&group(y);. . .} (el)", "eq_num": "(e2)" } ], "section": "The Structure of Background Knowledge", "sec_num": "3.2" }, { "text": "and e2 ~enter el.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The Structure of Background Knowledge", "sec_num": "3.2" }, { "text": "Two things should be explained now about this notation:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The Structure of Background Knowledge", "sec_num": "3.2" }, { "text": "Meanings of predicates/words are represented on the right-hand sides of the arrows as collections of formulas--i.e., theories. The main idea is that these mini-theories of predicates appearing in a paragraph will jointly provide enough constraints to exclude implausible interpretations. (One can think of meanings as regions in space, and of constraints as sets of linear inequalities approximating these regions). How this can be done, we will show in a moment.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The Structure of Background Knowledge", "sec_num": "3.2" }, { "text": "These theories are partially ordered; and their partial orders are written as \"music\" > ~. More specific paths are preferred: Assuming that all higher paths, like path (1), are excluded by inconsistency, path (2) is the most plausible interpretation of c~&fl, and it is preferred to (3). (More explanations in the text).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Figure 2", "sec_num": null }, { "text": "To make Figure 2 more intuitive we assigned some meanings to the partial orders. Thus, (1 represents some possible meanings of \"flag,\" shown with the help of the \"key words;\" the meaning \"piece of cloth\" preferred to \"deer's tail.\" The word \"strike\" has dozens of meanings, and we can imagine that the meaning of the transitive verb being represented by (2, with \"hit in anger\" at the top, then \"hit, e.g. a ball\" and \"discover\" equally preferred, and then all other possible meanings. The trivial (3 representing \"strike a flag\" should remind us that we already know all that from Section 3.2. Notice that path (2) does not give us the correct interpretation of \"strike the flag,\" which is created from \"cloth\"~-\"lower.\"", "cite_spans": [], "ref_spans": [ { "start": 8, "end": 16, "text": "Figure 2", "ref_id": "FIGREF3" } ], "eq_spans": [], "section": "Figure 2", "sec_num": null }, { "text": "Each element of the cartesian product I-[ = M2, if M1, satisfies more R + M-abductible equalities than M2. The principle articulating preference for having the references resolved can now be expressed as", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Definition", "sec_num": null }, { "text": "Assume that T E PT(P) is a partial theory of a paragraph P. Every preferred model M E PM(T) is a maximal element of the ordering >= of Mods(T).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Metarule 1", "sec_num": null }, { "text": "To explain the meaning of the metarule, let us analyze the paragraph (P1, P2, P3) and the background knowledge needed for some kind of rudimentary understanding of that text. The rule (i_1) (infection is a result of being infected by a disease... ), dealing with the infection i, introduces a disease dl; we also know about the existence of the disease d in 1347. Now, notice that there may be many models satisfying the object theory of the paragraph P augmented by the background knowledge. But we can find two among them: in one, call it M1, d and dl are identical; in the other one, M2, they are distinct. The rule says that only the first one has a chance to be a preferred model of the paragraph; it has more noun phrase references resolved than the other model, or--formally--it satisfies more R + M-abductible equalities, and therefore M1 >= M2.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Metarule 1", "sec_num": null }, { "text": "This reasoning, as the reader surely has noticed, resembles the example about infections from the beginning of this section. The difference between the cases lies in the equality d = dl being the result of a formal choice of a model, while i = i ~ wasn't proved, just \"reasonably\" assumed.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Metarule 1", "sec_num": null }, { "text": "In interpreting texts, knowledge of typical subjects and typical objects of verbs helps in anaphora resolution (cf. Braden-Harder & Zadrozny 1990) . Thus if we know that A farmer grows vegetables, either having obtained this information directly from a text, or from R, we can reasonably assume tlhat He also grows some cotton refers to the farmer, and not to a policeman mentioned in the same paragraph. Of course, this should be only a defeasible assumption, if nothing indicates otherwise. We now want to express this strategy as a metarule:", "cite_spans": [ { "start": 111, "end": 146, "text": "(cf. Braden-Harder & Zadrozny 1990)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Metarule 1", "sec_num": null }, { "text": "Let us assume that it is known that P(a, b) & Q(a) & R(b), and it is not known that P(a', X), for any X. Then models in which P(a, c) & R'(c) holds are preferred to models in which P(a',c) & R'(c) is true.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Metarule 2", "sec_num": null }, { "text": "One can think of this rule as a model-theoretic version of Ockham's razor or abduction; it says \"minimize the number of things that have the property P(,, ,),\" and it allows us to draw certain conclusions on the basis of partial information. We shall see it in action in Section 5.2.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Metarule 2", "sec_num": null }, { "text": "We have no doubts that various other metarules will be necessary; clearly, our two metarules cannot constitute the whole theory of anaphora resolution. They are intended as an illustration of the power of abduction, which in this framework helps determine the universe of the model (that is the set of entities that appear in it). Other factors, such as the role of focus (Grosz 1977 (Grosz , 1978 Sidner 1983) or quantifier scoping (Webber 1983 ) must play a role, too. Determining the relative importance of those factors, the above metarules, and syntactic clues, appears to be an interesting topic in itself.", "cite_spans": [ { "start": 372, "end": 383, "text": "(Grosz 1977", "ref_id": "BIBREF18" }, { "start": 384, "end": 397, "text": "(Grosz , 1978", "ref_id": "BIBREF17" }, { "start": 398, "end": 410, "text": "Sidner 1983)", "ref_id": "BIBREF56" }, { "start": 433, "end": 445, "text": "(Webber 1983", "ref_id": "BIBREF64" } ], "ref_spans": [], "eq_spans": [], "section": "Metarule 2", "sec_num": null }, { "text": "Note: In our translation from English to logic we are assuming that \"it\" is anaphoric (with the pronoun following the element that it refers to), not cataphoric (the other way around). This means that the \"it\" that brought the disease in P1 will not be considered to refer to the infection \"i\" or the death \"d\" in P3. This strategy is certainly the right one to start out with, since anaphora is always the more typical direction of reference in English prose (Halliday and Hasan 1976, p. 329) .", "cite_spans": [ { "start": 460, "end": 493, "text": "(Halliday and Hasan 1976, p. 329)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Metarule 2", "sec_num": null }, { "text": "Since techniques developed elsewhere may prove useful, at least for comparison, it is worth mentioning at this point that the proposed metarules are distant cousins of \"unique-name assumption\" (Genesereth and Nilsson 1987) , \"domain closure assumption\" (ibid.), \"domain circumscription\" (cf. Etherington and Mercer 1987) , and their kin. Similarly, the notion of R + M-abduction is spiritually related to the \"abductive inference\" of Reggia (1985) , the \"diagnosis from first principles\" of Reiter (1987) , \"explainability\" of Poole (1988) , and the subset principle of Berwick (1986) . But, obviously, trying to establish precise connections for the metarules or the provability and the R + M-abduction would go much beyond the scope of an argument for the correspondence of paragraphs and models. These connections are being examined elsewhere (Zadrozny forthcoming).", "cite_spans": [ { "start": 193, "end": 222, "text": "(Genesereth and Nilsson 1987)", "ref_id": "BIBREF12" }, { "start": 292, "end": 320, "text": "Etherington and Mercer 1987)", "ref_id": "BIBREF9" }, { "start": 434, "end": 447, "text": "Reggia (1985)", "ref_id": "BIBREF54" }, { "start": 491, "end": 504, "text": "Reiter (1987)", "ref_id": "BIBREF55" }, { "start": 527, "end": 539, "text": "Poole (1988)", "ref_id": "BIBREF52" }, { "start": 570, "end": 584, "text": "Berwick (1986)", "ref_id": "BIBREF0" } ], "ref_spans": [], "eq_spans": [], "section": "Metarule 2", "sec_num": null }, { "text": "The construction of a model of a paragraph, a p-model, must be based on the information contained in the paragraph itself (the object theory) and in the referential level while the metalevel restricts ways that the model can be constructed, or, in other words, provides criteria for choosing a most plausible model(s), if a partial theory is ambiguous. This role of the metarules will be clearly visible in finding references of pronouns in a simple case requiring only a rule postulating that these references be searched for, and in a more complex case (in Section 5) when they can be found only by an interplay of background knowledge and (a formalization of) Gricean maxims.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "p-Models", "sec_num": "5.2" }, { "text": "M is a p-model of a paragraph P iff there exists a coherent partial theory T E PT(P) such that M E PM(T).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Definition", "sec_num": null }, { "text": "Having defined the notion of a p-model, we can mimic now, in logic, the reasoning presented in Section 2.2. Using background information and the translation of sentences, we build a p-model of the paragraph. This involves determining the references of the pronoun \"it,\" and deciding whether \"struck\" in the sentence It struck rapidly means \"hit\" (slb) or \"harmed\" (s2_ex). We have then two meanings of \"strike\" and a number of possibilities for the pronouns.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Definition", "sec_num": null }, { "text": "We begin by constructing the two classes of preferred models given by (slb) and (s2_ex), respectively. It is easily seen that, in the models of the first class, based on {$2, slb}, (that is {rapidly:strike(yo) and strike(x) --~ hit(x)...}), together with all other available information, do not let us R+M-abduct anything about y0, i.e., the referent for the subject pronoun \"it\" in P2 (it struck rapidly). On the other hand, from {$2, s2_ex, dl} we R + M-abduct that y0 = d, i.e. the disease struck rapidly. That is the case because s2_ex implies that the agent that \"struck rapidly\" is actually an illness. 1we conclude that Y0 --d. In other words, the referent for the subject \"it\" is \"disease.\" Thus the Metarule (1) immediately eliminates all the models from the first class given by (slb), in which \"struck\" means \"hit.\"", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Definition", "sec_num": null }, { "text": "Notice that we cannot prove in classical logic that the ship has brought the disease. But we are allowed to assume it by the above formal rule as the most plausible state of affairs, or--in other words--we prove it in our three-level logic.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Definition", "sec_num": null }, { "text": "We are left then with models of the three sentences ($1, $2, $3) that contain {$2, s2_ex, dl}; they all satisfy y0 = d. We now use {Sl, shl,bl}(enter(s,m . From these facts we can conclude by Metarule (1) that x0 = s: a \"ship\" is an agent that carries goods; to \"bring\" means to \"carry\"; and the disease has been brought by something-we obtain carry (xo, d) and carry(s, y); and then by Metarule (2), carry (s, d) . That is, the referent for the pronoun \"it\" in P1 (... bringing with it the disease... ) should be \"ship.\"", "cite_spans": [ { "start": 136, "end": 153, "text": "shl,bl}(enter(s,m", "ref_id": null }, { "start": 350, "end": 357, "text": "(xo, d)", "ref_id": null }, { "start": 407, "end": 413, "text": "(s, d)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Definition", "sec_num": null }, { "text": "Observe that we do not assert about the disease that it is a kind of goods or people; the line of reasoning goes as follows: since ships are known to carry people or goods, and ports are not known to carry anything, we may assume that the ship carried the disease along with its standard cargo.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Definition", "sec_num": null }, { "text": "Having resolved all pronoun references, with no ambiguity left, we conclude that the class PM(P) consists of only one model, based on the the partial theory {$1, $2, $3, shl, bl, e_l, s2_ex, dl, de1, il, al, ctl}. The model describes a situation in which the ship came into the port/harbor; the ship brought the disease; the disease was caused by an infection; the disease harmed rapidly, causing a painful death; and so on.", "cite_spans": [ { "start": 157, "end": 213, "text": "{$1, $2, $3, shl, bl, e_l, s2_ex, dl, de1, il, al, ctl}.", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Definition", "sec_num": null }, { "text": "The topic Tp of (P1, P2, P3) is the disease(x). The first sentence talks about it; the second one refers to it using the pronoun \"it,\" and the third one extends our knowledge about the topic, since \"disease' is linked to \"infection\" through dl. Furthermore, ", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Definition", "sec_num": null }, { "text": "The p-model for the example paragraph \"disease\" is the only noun phrase mentioned or referred to in all three sentences; the sentence $1 is the topic sentence. The p-model of the paragraph is represented by Figure 3 . But notice that our definition of topic licences also other analyses, for example, one in which all the predicates of the first sentence constitute the topic of the paragraph, $2 elaborates $1 (in the sense of condition I (c) of the definition of topic), and $3 elaborates $2. Based on the larger context, we prefer the first analysis; however, a computational criterion for such a preference remains as an open problem.", "cite_spans": [], "ref_spans": [ { "start": 207, "end": 215, "text": "Figure 3", "ref_id": "FIGREF3" } ], "eq_spans": [], "section": "Figure 3", "sec_num": null }, { "text": "We have already seen examples of the application of metalevel rules. In the analysis of the paragraph, we applied one such rule expressing our commonsense knowledge about the usage of pronouns. In this section we discuss two other sources of metalevel axioms: Gricean cooperative principles, which reduce the number of possible interpretations of a text or an utterance; and connectives and modalities--such as \"but, .... unless,\" or \"maybe\"---which refer to the process of constructing the models or partial theories, and to some operations on them (see Figure 4) .", "cite_spans": [], "ref_spans": [ { "start": 555, "end": 564, "text": "Figure 4)", "ref_id": "FIGREF3" } ], "eq_spans": [], "section": "On the Role of the Metalevel", "sec_num": "6." }, { "text": "We can see then two applications of metarules: in constructing models of a text from representations of sentences, and in reducing, or constraining, the ambiguity of the obtained structure. We begin by showing how to formalize the latter. In the next subsection (6.1), assuming the Gricean maxims to be constraints on language communication, either spoken or written, we use their formal versions in building partial theories. A specific instance of the rule of \"quantity\" turns out to be applicable to anaphora resolution. That example will end our discussion of anaphora in this article.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "On the Role of the Metalevel", "sec_num": "6." }, { "text": "The last topic we intend to tackle is the semantic role of conjunctions. In subsection 6.2 we present a metalevel axiom dealing with the semantic role of the adversative conjunction \"but;\" then we talk about some of its consequences for constructing models of text. This will complete our investigation of the most important issues concerning paragraph structure: coherence (how one can determine that a paragraph expresses a \"thought'0, anaphora (how one can compute \"links\" between entities that a paragraph talks about), and cohesion (what makes a paragraph more than just a sum of sentences). Of course, we will not have final answers to any of these problems, but we do believe that the/a direction of search for computational models of text will be visible at that point.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "On the Role of the Metalevel", "sec_num": "6." }, { "text": "We assume a flat structure of the metalevel, envisioning it as a collection of (closed) formulas written in the language of set theory or higher order logic. In either of the two theories it is possible to define the notions of a model, satisfiability, provability, etc. for any first order language (cf. e.g. Shoenfield 1967) ; therefore the metalevel formulas can say how partial theories should be constructed (specifying for instance the meaning of 0) and what kinds of models are admissible. The metarules thus form a logical theory in a special language, such as the language of ZF-set theory. However, for the sake of readability, we express all of them in English.", "cite_spans": [ { "start": 310, "end": 326, "text": "Shoenfield 1967)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "On the Role of the Metalevel", "sec_num": "6." }, { "text": "A Gricean Cooperative Principle applies to text, too. For instance, in normal writing people do not express common knowledge about typical functions of objects. In fact, as the reader may check for himself, there is nothing in Gricean maxims that does not apply to written language. That the maxims play a semantic role is hardly surprising. But that they can be axiomatized and used in building formal models of texts is new. We present in the next couple of paragraphs our formalization of the first maxim, and sketch axiomatizations of the others. Then we will apply the formal rule in an example.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Formalization of Gricean Maxims", "sec_num": "6.1" }, { "text": "Gricean maxims, after formalization, belong to the rnetalevel. This can be seen from our formalization of the rule \"don't say too much.\" To this end we define redundancy of a partial theory T of a paragraph as the situation in which some sentences can be logically derived from other sentences and from the theory T in a direct manner:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Formalization of Gricean Maxims", "sec_num": "6.1" }, { "text": "(3S E/5)(3cr E R)[a E T& e : ~b --~ ~b &/St-~ & {~} U (/5-{S}) F-S]", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Formalization of Gricean Maxims", "sec_num": "6.1" }, { "text": "The meaning of this formula can be explained as follows: a paragraph P has been translated into its formal version/5 and is to be examined for redundancy. Its partial theory PT(/5) has also been computed. The test will turn positive if, for some sentence S, we can find a rule/theorem a = ~ --* ~ in PT(P) such that the sentence S is implied (in a classical logic) by the other sentences and ~. For example, if the paragraph about Black Death were to contain also the sentence The ship carried people or goods, or", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Formalization of Gricean Maxims", "sec_num": "6.1" }, { "text": "\u2022 Quantity. Say neither too much nor too little.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Formalization of Gricean Maxims", "sec_num": "6.1" }, { "text": "\u2022 Quality. Try to make your contribution one that is true.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Formalization of Gricean Maxims", "sec_num": "6.1" }, { "text": "\u2022 Relation. Be relevant.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Formalization of Gricean Maxims", "sec_num": "6.1" }, { "text": "\u2022 Manner. Avoid obscurity and ambiguity; be brief and orderly.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "A Formalization of Gricean Maxims", "sec_num": "6.1" }, { "text": "The Gricean maxims both, which (in its logical form) belongs to R, it would be redundant: ~ = (shl), there.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Figure 4", "sec_num": null }, { "text": "Similarly, the definition takes care of the redundancy resulting from a simple repetition.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Figure 4", "sec_num": null }, { "text": "Metarule Gla (nonredundancy) If T1, T2 C PT(P) and T1 is less redundant than T2, then the theory T1 is preferred to T2. (Where \"less redundant\" means that the number of redundant sentences in T1 is smaller than in T2) The relevant half of the Maxim of Quantity has been expressed by Gla. How would we express the other maxims? The \"too little\" part of the first maxim might be represented as a preference for unambiguous partial theories. The second maxim has been assumed all the time--when constructing partial theories or models, the sentences of a paragraph are assumed to be true. The Maxim of Manner seems to us to be more relevant for critiquing the style of a written passage or for natural language generation; in the case of text generation, it can be construed as a requirement that the produced text be coherent and cohesive.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Figure 4", "sec_num": null }, { "text": "We do not claim that Gla is the best or unique way of expressing the rule \"assume that the writer did not say too much.\" Rather, we stress the possibility that one can axiomatize and productively use such a rule. We shall see this in the next example: two sentences, regarded as a fragment of paragraph, are a variation on a theme by Hobbs (1979) .", "cite_spans": [ { "start": 334, "end": 346, "text": "Hobbs (1979)", "ref_id": "BIBREF28" } ], "ref_spans": [], "eq_spans": [], "section": "Figure 4", "sec_num": null }, { "text": "The above metarule postulating \"nonredundancy\" implies that \"he\" = \"the third officer, .... his\" = \"the captain's\" are the referents of the pronouns. This is because the formula", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Example 3 The captain is worried because the third officer can open his safe. He knows the combination.", "sec_num": null }, { "text": "belongs to R, since it is common knowledge about safes that they have owners, and also combinations that are known to the owners. Therefore \"his\" = \"the third officer's\" would produce a redundant formula, corresponding to the sentence The third officer can open the third officer's safe. By the same token, The captain knows the combination would be redundant too.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "safe(x) --, (owns(y~ x) & cmbntn(z~ x) --, knows(y~ z) & can_open(y~ x) ) E Tsafe,", "sec_num": null }, { "text": "We now explain the details of this reasoning. One first proves that \"his\" = \"the captain's.\" Indeed, if \"his\" = \"the third officer's,\" then our example sentence would mean We assume also, based on common knowledge about worrying, that worry(x', s') -~ S. That is, one worries about things that might possibly be or become true (S denotes the logical formula corresponding to the sentence s, cf. Section 3); but one doesn't worry about things that are accepted as (almost) always true (such as the law of gravity), so that worry(x', 's') ~ -~(S E Tf), where f ranges over subformulas of S.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "safe(x) --, (owns(y~ x) & cmbntn(z~ x) --, knows(y~ z) & can_open(y~ x) ) E Tsafe,", "sec_num": null }, { "text": "In our case, S immediately follows from Tsafe and X, where X = safe(sf) & third_officer(o) & owns(o, sf)--the fact that \"the third officer can open the third officer's safe\" is a consequence of general knowledge about the ownership of safes. And therefore the interpretation with \"his\" = \"the captain's\" is preferred as less redundant by the rule Gla. This theory contains representations of the two sentences, the theory of safes, a theory of worrying, and the equality \"his\" = \"captain's.\" It remains to prove that \"he\" = \"the third officer.\" Otherwise we have P1. The captain is worried because the third officer can open the captain's safe.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "safe(x) --, (owns(y~ x) & cmbntn(z~ x) --, knows(y~ z) & can_open(y~ x) ) E Tsafe,", "sec_num": null }, { "text": "P2. ? The captain knows the combination.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "safe(x) --, (owns(y~ x) & cmbntn(z~ x) --, knows(y~ z) & can_open(y~ x) ) E Tsafe,", "sec_num": null }, { "text": "Clearly, the last sentence is true but redundant--the theory of \"safe\" and P1 entail P2:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "safe(x) --, (owns(y~ x) & cmbntn(z~ x) --, knows(y~ z) & can_open(y~ x) ) E Tsafe,", "sec_num": null }, { "text": "We are left with the combination Q1. The captain is worried because the third officer can open the captain's safe.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "{P1} U Tsafe t-P2", "sec_num": null }, { "text": "Q2. ? The third officer knows the combination.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "{P1} U Tsafe t-P2", "sec_num": null }, { "text": "In this case, Q2 does not follow from {Q1} u Tsafe and therefore Q1, Q2 is preferred to P1, P2 (by Gla). We obtain then", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "{P1} U Tsafe t-P2", "sec_num": null }, { "text": "The captain is worried because the third officer can open the captain's safe.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "{P1} U Tsafe t-P2", "sec_num": null }, { "text": "as the most plausible interpretation of our example sentences. Note: The reader must have noticed that we did not bother to distinguish the sentences P1, P2, Q1 and Q2 from their logical forms. Representing \"because\" and \"know\" adequately should be considered a separate topic; representing the rest (in the first order convention of this paper) is trivial.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The third officer knows the combination", "sec_num": null }, { "text": "Can one deal effectively with the problem of reference without axiomatized Gricean maxims, for instance by using only \"petty conversational implicature\" (Hobbs 1979) , or the metarules of Section 5.2? It seems to us that the answer is no.", "cite_spans": [ { "start": 153, "end": 165, "text": "(Hobbs 1979)", "ref_id": "BIBREF28" } ], "ref_spans": [], "eq_spans": [], "section": "Was the Use of a Gricean Maxim Necessary?", "sec_num": "6.1.1" }, { "text": "As a case in point, consider the process of finding the antecedent of the anaphor \"he\" in the sentences John can open Bill's safe. He knows the combination. Hobbs (1979 Hobbs ( , 1982 proves \"he\" = \"John\" by assuming the relation of \"elaboration\" between the sentences. (Elaboration is a relation between two segments of a text. It intuitively means \"expressing the same thought from a different perspective,\" but has been defined formally as the existence of a proposition implied by both segments-here the proposition is \"John can open the safe\".) However, if we change the pair to the triple As we have observed, correct interpretations cannot be chosen by an interaction of an object level theory and a referential level alone, because coherence, plausibility and consistency are too weak to weed out wrong partial theories. Metarules are necessary. True, the captain knew the combination, but it was consistent that \"his\" might have referred to \"the third officer's.\"", "cite_spans": [ { "start": 157, "end": 168, "text": "Hobbs (1979", "ref_id": "BIBREF28" }, { "start": 169, "end": 183, "text": "Hobbs ( , 1982", "ref_id": "BIBREF27" } ], "ref_spans": [], "eq_spans": [], "section": "Was the Use of a Gricean Maxim Necessary?", "sec_num": "6.1.1" }, { "text": "Any analysis of natural language text, to be useful for a computational system, will have to deal with coherence, anaphora, and connectives. We have examined so far the first two concepts; we shall present now our view of connectives to complete the argument about paragraphs being counterparts of models. We present a metalevel rule that governs the behavior of the conjunction \"but;\" we formalize the manner in which \"but\" carries out the contradiction. Then we derive from it two rules that prevent infelicitous uses of \"but.\"", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Semantics of the Conjunction \"But\"", "sec_num": "6.2" }, { "text": "Connectives are function words--like conjunctions and some adverbs--that are responsible simultaneously for maintaining cohesiveness within the text and for signaling the nature of the relationships that hold between and among various text units. \"And,\" \"or,\" and \"but\" are the three main coordinating connectives in English. However, \"but\" does not behave quite like the other two--semantically, \"but\" signals a contradiction, and in this role it seems to have three subfunctions: . . Opposition (called \"adversative\" or \"contrary-to-expectation\" by Halliday and Hasan 1976; cf. also Quirk et al. 1972, p. 672) .", "cite_spans": [ { "start": 551, "end": 575, "text": "Halliday and Hasan 1976;", "ref_id": null }, { "start": 576, "end": 611, "text": "cf. also Quirk et al. 1972, p. 672)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Semantics of the Conjunction \"But\"", "sec_num": "6.2" }, { "text": "Comparison. In this function, the first conjunct is not so directly contradicted by the second. A contradiction exists, but we may have to go through additional levels of implication to find it. Consider the sentence:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The ship arrived but the passengers could not get off. The yacht is cheap but elegant.", "sec_num": null }, { "text": ". That basketball player is short, but he's very quick.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The ship arrived but the passengers could not get off. The yacht is cheap but elegant.", "sec_num": null }, { "text": "Affirmation. This use of \"but\" always follows a negative clause, and actually augments the meaning of the preceding clause by adding supporting information:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The ship arrived but the passengers could not get off. The yacht is cheap but elegant.", "sec_num": null }, { "text": "The disease not only killed thousands of people, but also ended a period of economic welfare.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The ship arrived but the passengers could not get off. The yacht is cheap but elegant.", "sec_num": null }, { "text": "In this section we consider only the first, or adversative, function of the coordinating conjunction \"but.\" 6.2.1 The Semantic Function of \"But\" \"But\" introduces an element of surprise into discourse. Because it expresses some kind of contradiction, \"but\" has no role in the propositional calculus equivalent to the roles filled by \"and\" and \"or.\" Although there are logical formation rules using the conjunction operator (\"and\") and the disjunction operator (\"or\"), there is no \"but\" operator. What, then, is the semantic role of \"but\"?", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The ship arrived but the passengers could not get off. The yacht is cheap but elegant.", "sec_num": null }, { "text": "We believe that its function should be described at the metalevel as one of many rules guiding the construction of partial theories. This is expressed below.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "The ship arrived but the passengers could not get off. The yacht is cheap but elegant.", "sec_num": null }, { "text": "The formulas \u2022 but k~, ~' but ~1 .... of a (formal representation of) paragraph P are to be interpreted as follows:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Metarule (BUT)", "sec_num": null }, { "text": "In the construction of any T E PT(P) instead of taking @f to be the union U of rr --* T~, take the union of ~ --* T\u00a2/{k~, ~',...}.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Metarule (BUT)", "sec_num": null }, { "text": "The symbol cr ---* T~,/{qt, \u00a2d',...} denotes a maximal consistent with {or, ~, k~',...} subtheory of r~ --* T\u00a2, and in general T/T t will be a maximal consistent with T' subtheory of T.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Metarule (BUT)", "sec_num": null }, { "text": "\"But\" is then an order to delete from background information everything contradicting \u2022 , but to use what remains. Notice that \"and\" does not have this meaning; a model for \u2022 and \u2022 will not contain any part of a theory that contradicts either of the clauses \u2022 or \u00a2d.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Metarule (BUT)", "sec_num": null }, { "text": "Typically this rule will be used to override defaults, to say that the expected consequences of the first conjunct hold except for the fact expressed by the second conjunct; for instance: We were coming to see you, but it rained (so we didn't). The rule BUT is supposed to capture the \"contrary-to-expectation\" function of \"but.\"", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Metarule (BUT)", "sec_num": null }, { "text": "We present now a simple example of building a model of a one-sentence paragraph containing \"but.\" We will use this example to explain how the rule BUT can be used. Using background information presented below, we will construct a partial model for this one-sentence paragraph. tion; their validity indirectly supports the plausibility of our analysis of \"but.\" BUT_C1 : ff but -~ is incorrect, if \u2022 --* \u2022 is a \"law.\" e.g. Henry was murdered but not killed.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Metarule (BUT)", "sec_num": null }, { "text": "Our referential level is a collection of partially ordered theories; we have expressed the fact that a theory of some \u00a2 is a \"law\" is by deleting the empty interpretation of \u00a2 from the partial order. If we accept the definition of a concept as given by necessary and sufficient conditions, the theories would all appear as laws. If we subscribe to a more realistic view where definitions are given by a collection of central/prototypical and peripheral conditions, only the peripheral ones can be contradicted by \"but.\" In either formalization we get BUT_C1 as a consequence: Since \"laws\" cannot be deleted, BUT can't be applied, and hence its use in those kinds of sentences would be incorrect.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Metarule (BUT)", "sec_num": null }, { "text": "W. Labov (1973) discussed sentences of the form ,This is a chair but you can sit on it.", "cite_spans": [ { "start": 3, "end": 15, "text": "Labov (1973)", "ref_id": "BIBREF39" } ], "ref_spans": [], "eq_spans": [], "section": "Metarule (BUT)", "sec_num": null }, { "text": "The sentence is incorrect, since the function \"one can sit on it\" belongs to the core of the concept \"chair\"; so--contrary to the role of \"but\"--the sentence does not contain any surprising new elements. Using the Metarule (BUT) and the cooperative principle of Grice, we get BUT_C2: \u2022 but \u2022 is incorrect, if \u2022 -* k~ is a \"law.\"", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Metarule (BUT)", "sec_num": null }, { "text": "The Metarule (BUT) gives the semantics of \"but;\" the rules BUT_C1 and BUT_C2 follow from it (after formalization in a sufficiently strong rnetalanguage such as type theory or set theory). We can link all of them to procedures for constructing and evaluating models of text. Are they sufficient? Certainly not. We have not dealt with the other usages of '%ut;\" neither have we shown how to deal with the apparent asymmetry of conclusions: cheap but elegant seems to imply \"worth buying,\" but elegant but cheap doesn't; we have ignored possible prototypical effects in our semantics. However, we do believe that other rules, dealing with \"but\" or with other connectives, can be conveniently expressed in our framework. (The main idea is that one should talk explicitly and formally about relations between text and background knowledge, and that this knowledge is more than just a list of facts--it has structure, and it is ambiguous.) Furthermore, the semantics of \"but\" as described above is computationally tractable.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Metarule (BUT)", "sec_num": null }, { "text": "We also believe that one could not present a similarly natural account of the semantics of \"but\" in traditional logics, because classical logics withstand contradictions with great difficulty. Contradiction, however, is precisely what \"but\" expresses. Notice that certain types of coordinating conjunctions often have their counterparts in classical logic: copulative (and, or, neither-nor, besides, sometimes etc.) , disjunctive (like either-or), illative (hence, for that reason). Others, such as explanatory (namely or viz.) or causal (for) conjunctions can probably be expressed somehow, for better or worse, within a classical framework. Thus the class of adversative conjunctions (but, still, and yet, nevertheless) is in that sense unique.", "cite_spans": [ { "start": 368, "end": 415, "text": "(and, or, neither-nor, besides, sometimes etc.)", "ref_id": null }, { "start": 686, "end": 721, "text": "(but, still, and yet, nevertheless)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Metarule (BUT)", "sec_num": null }, { "text": "We hope that the reader has found this paper coherent, and its topic--the correspondence between paragraphs and models--interesting. Our strategy was to divide the subject into three subtopics: a theory of anaphora, which corresponds to the logical theory of equality in p-models; a theory of background knowledge, expressed as the logical theory of reference in the three-level semantics; and principles of communication encoded in metarules. These principles include Gricean maxims and the semantics of cohesion, and specify a model theory for the three-level semantics. The framework resulting from putting these theories together is computational, empirical, and verifiable (even if incomplete); furthermore, it has strong links to already existing natural language processing systems. In particular, the new logical level--the referential level--is exemplified by on-line dictionaries and other reference works, from which we extract background information about defaults and plausibility rankings.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conclusions", "sec_num": "7." }, { "text": "We also hope that the reader would be inclined to share our belief that natural language text can be properly and usefully analyzed by means of a three-level semantics that includes an object level, a metalevel, and a referential level. We believe that the coherence of an essay, a paper, or a book can be described by an extension of our theory. The work of van Dijk and Kintch (1983) on \"macrostructures\" could probably form the basis for such an expansion. Similarly, much of the abovementioned work by Hobbs, Webber, Grosz, and Sidner can be incorporated into this framework.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conclusions", "sec_num": "7." }, { "text": "Our main intention was to demonstrate that formal notions of background knowledge can be used to", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conclusions", "sec_num": "7." }, { "text": "\u2022 define coherence, make it semantically distinct from mere consistency, and link it formally with the notion of a topic;", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conclusions", "sec_num": "7." }, { "text": "\u2022 define a class of p-models--logical models of paragraphs;", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conclusions", "sec_num": "7." }, { "text": "\u2022 provide a semantics for \"but\" (which exemplifies our understanding of grammatical cohesion);", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conclusions", "sec_num": "7." }, { "text": "\u2022 express the Gricean maxims formally, and use them in a computational model of communication (which seems to contradict Allen 1988, p. 464 ).", "cite_spans": [ { "start": 121, "end": 139, "text": "Allen 1988, p. 464", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Conclusions", "sec_num": "7." }, { "text": "Moreover, we tried to convince the reader that paragraph is an important linguistic unit, not only because of its pragmatic importance exemplified by coherence and links to background knowledge, but also because of its role in assignment of syntactic structures (viz. ellipsis) and in semantics (viz. its possible role in evaluating semantic representations). A great many issues have been omitted from our analysis. Thus, although we are aware that anaphora resolution and consistency depend on previously processed text, the problem of connecting a paragraph to such text has been conveniently ignored. Notice that this doesn't make our thesis about paragraphs being units of semantic processing any weaker, we have not claimed that paragraphs are independent. The questions of how to translate from natural language to a logical notation needs a lot of attention; we have merely assumed that this can be done. Continuing this list, we have accepted a very classical theory of meaning, given by Tarski: the truth is what is satisfied in a model. This theory should be refined, for instance by formalizing Lakoff's (1987) concept of radial categories, and proposing mechanisms for exploiting it. By the same token, the concept of reference has to be broadened to include iconic (e.g., visual and tactile) information. And certainly it would be .nice to have a more detailed theory describing the role of the metalevel. In particular, we can imagine that the simple structure of a collection of set theoretic formulas can be replaced by something more interesting. We leave this as another open problem.", "cite_spans": [ { "start": 1107, "end": 1122, "text": "Lakoff's (1987)", "ref_id": "BIBREF41" } ], "ref_spans": [], "eq_spans": [], "section": "Conclusions", "sec_num": "7." }, { "text": "We have shown that it is possible to develop a formal system with an explicit relationship between background knowledge and text, showing mechanisms that take advantage of preference, coherence, and contradiction (the reality of these phenomena has never been disputed, but their semantic functions had not been investigated). We should also mention that we have also begun some work on actually checking the empirical validity of this model (cf. e.g. Braden-Harder and Zadrozny 1990), using online dictionaries (LDOCE and Webster's) as the referential level. We know, of course, that existing dictionaries are very imperfect, but (1) they can be accessed and used by computer programs; (2) they are getting better, as they are very systematically created with help of computers (see Sinclair 1987 for an account of how COBUILD was constructed); (3) obviously, we can imagine useful new ones, like a Dictionary of Pragmatics; (4) we believe that we can explore the new inference mechanisms even in such unrefined environments.", "cite_spans": [ { "start": 784, "end": 797, "text": "Sinclair 1987", "ref_id": "BIBREF59" } ], "ref_spans": [], "eq_spans": [], "section": "Conclusions", "sec_num": "7." }, { "text": "Although the scheme we have proposed certainly needs further refinement, we believe that it is correct in two of its most important aspects: first, in the separation of current paragraph analysis (the object theory) from background information (the referential level); and second, in asserting that the function of a paragraph is to allow the building of a model of the situation described in the paragraph. This model can be stored, maybe modified, and subsequently used as a reference for processing following paragraphs.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conclusions", "sec_num": "7." }, { "text": "Finally, the paper can be viewed as an argument that the meaning of a sentence cannot be defined outside of a context, just as the truth value of a formula cannot be computed in a vacuum. A paragraph is the smallest example of such a context--it is \"a unit of thought.\"", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conclusions", "sec_num": "7." }, { "text": "J. Burke, The Day the UniverseChanged. 1986. Little, Brown & Co., Boston, Massachusetts, p. 55.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "", "sec_num": null } ], "back_matter": [ { "text": "We gratefully acknowledge the help provided by our anonymous but diligent referees, by Graeme Hirst and Susan McRoy, and by our many colleagues at IBM Research, all for whom helped us to avoid worst consequences of Murphy's Law during the writing of this paper.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Acknowledgments", "sec_num": null }, { "text": "This yacht is cheap, but it is elegant.Referential level (a fragment) cheap(x) --, {~elegant(x) ; poor_quality(x);-~expensive} (cl)Note: Compare (yl) with (cl); in (yl) smallness is a property of a ship; this would be more precisely expressed as yacht(x) --* [ship(x) ; property: small(x)]. This trick allows us not to conclude that \"a big ant is big,\" or \"a small elephant is small.\"We ignore the problem of multiple meanings (theories) of predicates, and assume the trivial ordering in which all formulas are equally preferred. (But note that (e_yl) is still preferred to (el) as a more specific theory of \"elegant;\" cf. In other words, the yacht in question is a poor quality small and elegant ship serving as an inexpensive status symbol. The partial model of the theory T is quite trivial: it consists of one entity representing the yacht and of a bunch of its attributes. However, the size of the model is not important here; what counts is the method of derivation of the partial theory.", "cite_spans": [ { "start": 79, "end": 95, "text": "--, {~elegant(x)", "ref_id": null }, { "start": 259, "end": 267, "text": "[ship(x)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Example 4", "sec_num": null }, { "text": "The Metarule (BUT) is supposed to capture the \"contrary-to-expectation\" function of \"but.\" The next two rules follow from our formaliza-", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Confirming the Analysis.", "sec_num": "6.2.2" } ], "bib_entries": { "BIBREF0": { "ref_id": "b0", "title": "Learning from Positive-Only Examples: The Subset Principle and Three Case Studies", "authors": [ { "first": "J", "middle": [], "last": "Allen", "suffix": "" }, { "first": "", "middle": [], "last": "Benjamin/Cummings", "suffix": "" }, { "first": "California", "middle": [], "last": "Park", "suffix": "" }, { "first": "R", "middle": [ "C" ], "last": "Berwick", "suffix": "" } ], "year": 1986, "venue": "Machine Learning Vol. II", "volume": "", "issue": "", "pages": "625--645", "other_ids": {}, "num": null, "urls": [], "raw_text": "Allen, J. 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Since (shl) and (bl) dominate (respectively) (sh2) and (b2), the path f, nt represents a more plausible interpretation than ft.", "uris": null, "num": null, "type_str": "figure" }, "FIGREF2": { "text": "(a) or (b) or (c) holds: (a) Direct reference to the topic: Tp C Pred(Si) (b) Indirect reference to the topic:If \u00a2 E Pred(Si) & (\u00a2 -~ T\u00a2) E T, then Tp C Pred(T\u00a2) (c)Direct reference to a previous sentence:If \u00a2 E Pred(Si) & (~ ~ T\u00a2) E T then Pred(Si_l)MPred(\u00a2 ~ TV~ ) # 9~2. Either (i) or (ii) is satisfied:(i) Existence of a topic sentence: Tp C Pred(Si), for some sentence Si; (ii) Existence of a topic sentence: a theory of Tp belongs to R, i.e. if 0 is the conjunction of predicates of Tp then 0 ~ To E R, for some To.", "uris": null, "num": null, "type_str": "figure" }, "FIGREF3": { "text": "Constants s, m, d, i, b, 1347 satisfying: ship(s), Messina(m), disease(d), infection(i), death(b), year(1347). (ii) Formulae $1: [time: year(1347); event : enter(s,m) & ship(s) & port(m) & bring(xo, d) & disease(d) & name(d, BlackDeath) & (Xo --s V x0 = d V x0 --m)] $2: time : past; event : rapidly: strike(yo) & (yo --s V yo = m V y0 --d)] $3: 3t, t'{[time : t; infection(i)] & [time: t' c (t, t + 24h); event :come(b) & death(b) & agonizing(b)]}", "uris": null, "num": null, "type_str": "figure" }, "FIGREF4": { "text": "Referential level (a fragment): ship(x) --, {large: boat(x); 3ycarry(x,y) & (people(y) v goods(y)) & agent(x);...} (shl) /* ship--a large boat for carrying people or goods on the sea */ bring(x, y) --* {carry(x, y); ...} (bl) strike(x, y) --* {hit(x, y); agent(x) & patient(y);...} strike(x) --~ {hit(x); agent(x);...} strike(x) --* {illness(x) & By suddenly:harm(x, y);...} /* bring--to carry */ (sla) (slb) /* strike---to hit */ (s2 _ex) /* strike---to harm suddenly; \"they were struck by illness */ disease(y) ---* {illness(y) & 3z (infection(z) & causes(z,y));...} (dl) /* disease illness caused by an infection */ death(x) --~ {3t, y[x =' [time:t; event :die(y) & (ereature.(y) v plant(y))]']} (de_l) /* death--an event in which a creature or a plant dies */ come(x) --* {3t[time : t; event :arrive(x)]} (ct_l) /* to come--to arrive (...) in the course of time */ infection(x) --~ {3e, y, z[e = event :infect(y, z) & person(y) & disease(z))] & x --result(e)} (i_1) /* infection--the result of being infected by a disease */ agonizing(x) ~ {3y causes(x, y) & pain(y)} (a_l) /* agonizing---causing great pain */ enter(x, y) -. {come_in(x, y); place(y)} (e_l) /* enter--to come into a place */", "uris": null, "num": null, "type_str": "figure" }, "FIGREF5": { "text": "From rapidly : strike(yo), strike(x) -* illness(x) & .... disease(y) --, illness(y) & .... and disease(d) we can infer illness(yo) and illness(d); by the Metarule", "uris": null, "num": null, "type_str": "figure" }, "FIGREF6": { "text": ") & ship(s) & bring(xo~ d) & ...; ship(s) --~ (3y)carry(s,y) & ...; Vz[bring(xo, z) --* carry(xo, z)])", "uris": null, "num": null, "type_str": "figure" }, "FIGREF8": { "text": "The captain is worried because the third officer can open the third officer's safe; in logic: captain(x) & worry(x,s) & sentence(s) & s = 'the third officer can open the third officer's safe.\"", "uris": null, "num": null, "type_str": "figure" }, "FIGREF9": { "text": "Bill has a safe under the painting of his yacht. John can open Bill's safe. He knows the combination the relation of elaboration holds between the segment consisting of the first two sentences of the triple and each of the two possible readings: John knows the combination and Bill knows the combination. In this case, elaboration cannot choose the correct referent, but the rule Gla can and does. Clearly, an elaboration should not degenerate into redundancy; the Gricean maxims are to keep it fresh.", "uris": null, "num": null, "type_str": "figure" } } } }