{ "paper_id": "J87-3004", "header": { "generated_with": "S2ORC 1.0.0", "date_generated": "2023-01-19T02:55:02.020630Z" }, "title": "COMMONSENSE METAPHYSICS AND LEXICAL SEMANTICS", "authors": [ { "first": "Jerry", "middle": [ "R" ], "last": "Hobbs", "suffix": "", "affiliation": {}, "email": "" }, { "first": "William", "middle": [], "last": "Croft", "suffix": "", "affiliation": {}, "email": "" }, { "first": "Todd", "middle": [], "last": "Davies", "suffix": "", "affiliation": {}, "email": "" } ], "year": "", "venue": null, "identifiers": {}, "abstract": "In the TACITUS project for using commonsense knowledge in the understanding of texts about mechanical devices and their failures, we have been developing various commonsense theories that are needed to mediate between the way we talk about the behavior of such devices and causal models of their operation. Of central importance in this effort is the axiomatization of what might be called \"commonsense metaphysics\". This includes a number of areas that figure in virtually every domain of discourse, such as granularity, scales, time, space, material, physical objects, shape, causality, functionality, and force. Our effort has been to construct core theories of each of these areas, and then to define, or at least characterize, a large number of lexical items in terms provided by the core theories. In this paper we discuss our methodological principles and describe the key ideas in the various domains we are investigating.", "pdf_parse": { "paper_id": "J87-3004", "_pdf_hash": "", "abstract": [ { "text": "In the TACITUS project for using commonsense knowledge in the understanding of texts about mechanical devices and their failures, we have been developing various commonsense theories that are needed to mediate between the way we talk about the behavior of such devices and causal models of their operation. Of central importance in this effort is the axiomatization of what might be called \"commonsense metaphysics\". This includes a number of areas that figure in virtually every domain of discourse, such as granularity, scales, time, space, material, physical objects, shape, causality, functionality, and force. Our effort has been to construct core theories of each of these areas, and then to define, or at least characterize, a large number of lexical items in terms provided by the core theories. In this paper we discuss our methodological principles and describe the key ideas in the various domains we are investigating.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Abstract", "sec_num": null } ], "body_text": [ { "text": "In the TACITUS project for using commonsense knowledge in the understanding of texts about mechanical devices and their failures, we have been developing various commonsense theories that are needed to mediate between the way we talk about the behavior of such devices and causal models of their operation. Of central importance in this effort is the axiomatization of what might be called \"commonsense metaphysics\". This includes a number of areas that figure in virtually every domain of discourse, such as scalar notions, granularity, time, space, material, physical objects, causality, functionality, force, and shape. Our approach to lexical semantics is to construct core theories of each of these areas, and then to define, or at least characterize, a large number of lexical items in terms provided by the core theories. In the TACITUS system, processes for solving pragmatics problems posed by a text will use the knowledge base consisting of these theories, in conjunction with the logical forms of the sentences in the text, to produce an interpretation. In this paper we do not stress these interpretation processes; this is another, important aspect of the TACITUS project, and it will be described in subsequent papers (Hobbs and Martin, 1987) .", "cite_spans": [ { "start": 1233, "end": 1257, "text": "(Hobbs and Martin, 1987)", "ref_id": "BIBREF13" } ], "ref_spans": [], "eq_spans": [], "section": "INTRODUCTION", "sec_num": "1." }, { "text": "This work represents a convergence of research in lexical semantics in linguistics and efforts in artificial intelligence to encode commonsense knowledge. Over the years, lexical semanticists have developed formalisms of increasing adequacy for encoding word meaning, progressing from simple sets of features (Katz and Fodor, 1963) to notations for predicate-argument structure (Lakoff, 1972; Miller and Johnson-Laird, 1976 ), but the early attempts still limited access to world knowledge and assumed only very restricted sorts of processing. Workers in computational linguistics introduced inference (Rieger, 1974; Schank, 1975) and other complex cognitive processes (Herskovits, 1982) into our understanding of the role of word meaning. Recently linguists have given greater attention to the cognitive processes that would operate on their representations (e.g., Talmy, 1983; Croft, 1986) . Independently, in artificial intelligence an effort arose to encode large amounts of commonsense knowledge (Hayes, 1979; Hobbs and Moore, 1985; . The research reported here represents a convergence of these various developments. By constructing core theories of certain fundamental phenomena and defining lexical items within these theories, using the full power of predicate calculus, we are able to cope with complexities of word meaning that have hitherto escaped lexical semanticists. Moreover, we can do this within a framework that gives full scope to the planning and reasoning processes that manipulate representations of word meaning.", "cite_spans": [ { "start": 309, "end": 331, "text": "(Katz and Fodor, 1963)", "ref_id": "BIBREF14" }, { "start": 378, "end": 392, "text": "(Lakoff, 1972;", "ref_id": "BIBREF15" }, { "start": 393, "end": 423, "text": "Miller and Johnson-Laird, 1976", "ref_id": "BIBREF17" }, { "start": 602, "end": 616, "text": "(Rieger, 1974;", "ref_id": "BIBREF18" }, { "start": 617, "end": 630, "text": "Schank, 1975)", "ref_id": "BIBREF19" }, { "start": 669, "end": 687, "text": "(Herskovits, 1982)", "ref_id": "BIBREF6" }, { "start": 866, "end": 878, "text": "Talmy, 1983;", "ref_id": "BIBREF22" }, { "start": 879, "end": 891, "text": "Croft, 1986)", "ref_id": "BIBREF1" }, { "start": 1001, "end": 1014, "text": "(Hayes, 1979;", "ref_id": "BIBREF5" }, { "start": 1015, "end": 1037, "text": "Hobbs and Moore, 1985;", "ref_id": "BIBREF11" } ], "ref_spans": [], "eq_spans": [], "section": "INTRODUCTION", "sec_num": "1." }, { "text": "In constructing the core theories we are attempting to adhere to several methodological principles: 1. One should aim for characterization of concepts, rather than definition. One cannot generally expect to find necessary and sufficient conditions for a concept. The most we can hope for is to find a number of necessary conditions and a number of sufficient conditions. This amounts to saying that a great many predicates are primitives, but they are primitives that are highly interrelated with the rest of the knowledge base.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "INTRODUCTION", "sec_num": "1." }, { "text": "2. One should determine the minimal structure necessary for a concept to make sense. In efforts to axiomatize an area, there are two positions one may take, exemplified by set theory and by group theory. In axiomatizing set theory, one attempts to capture exactly some concept that one has strong intuitions about. If the axiomatization turns out to have unexpected models, this exposes an inadequacy. In group theory, by contrast, one characterizes an abstract class of structures. If it turns out that there are unexpected models, this is a serendipitous discovery of a new phenomenon that we can reason about using an old theory. The pervasive character of metaphor in natural language discourse shows that our commonsense theories of the world ought to be much more like group theory than set theory. By seeking minimal structures in axiomatizing concepts, we optimize the possibilities of using the theories in metaphorical and analogical contexts. This principle is illustrated below in the section on regions. One consequence of this principle is that our approach will seem more syntactic than semantic. We have concentrated more on specifying axioms than on constrncting models. Our view is that the chief role of models in our effort is for proving the consistency and independence of sets of axioms, and for showing their adequacy. As an example of the lastpoint, many of the spatial and temporal theories we construct are intended at least to have Euclidean space or the real numbers as one model, and a subclass of graph-theoretical structures as other models.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "INTRODUCTION", "sec_num": "1." }, { "text": "3. A balance must be struck between attempting to cover all cases and aiming only for the prototypical cases. In general, we have tried to cover as many cases as possible with an elegant axiomatization, in line with the two previous principles, but where the formalization begins to look baroque, we assume that higher processes will block some inferences in the marginal cases. We assume that inferences will be drawn in a controlled fashion. Thus, every outr6, highly context-dependent counterexample need not be accounted for, and to a certain extent, definitions can be geared specifically to a prototype.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "INTRODUCTION", "sec_num": "1." }, { "text": "4. Where competing ontologies suggest themselves in a domain, one should try to construct a theory that accommodates both. Rather than commit oneself to adopting one set of primitives rather than another, one should show how either set can be characterized in terms of the other. Generally, each of the ontologies is useful for different purposes, and it is convenient to be able to appeal to both. Our treatment of time illustrates this.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "INTRODUCTION", "sec_num": "1." }, { "text": "5. The theories one constructs should be richer in axioms than in theorems. In mathematics, one expects to state half a dozen axioms and prove dozens of theorems from them. In encoding commonsense knowledge, it seems to be just the opposite. The theorems we seek to prove on the basis of these axioms are theorems about specific situations that are to be interpreted, in particular, theorems about a text that the system is attempting to understand. 6. One should avoid falling into \"black holes\". There are a few \"mysterious\" concepts that crop up repeatedly in the formalization of commonsense metaphysics. Among these are \"relevant\" (that is, relevant to the task at hand) and \"normative\" (that is, conforming to some norm or pattern). To insist upon giving a satisfactory analysis of these before using them in analyzing other concepts is to cross the event horizon that separates lexical semantics from philosophy. On the other hand, our experience suggests that to avoid their use entirely is crippling; the lexical semantics of a wide variety of other terms depends upon them. Instead, we have decided to leave them minimally analyzed for the moment and use them without scruple in the analysis of other commonsense concepts. This approach will allow us to accumulate many examples of the use of these mysterious concepts, and in the end, contribute to their successful analysis. The use of these concepts appears below in the discussions of the words \"immediately\", \"sample\", and \"operate\".", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "INTRODUCTION", "sec_num": "1." }, { "text": "We chose as an initial target the problem of encoding the commonsense knowledge that underlies the concept of \"wear\", as in a part of a device wearing out. Our aim was to define \"wear\" in terms of predicates characterized elsewhere in the knowledge base and to be able to infer some consequences of wear. For something to wear, we decided, is for it to lose imperceptible bits of material from its surface due to abrasive action over time. One goal, which we have not yet achieved, is to be able to prove as a theorem that, since the shape of a part of a mechanical device is often functional and since loss of material can result in a change of shape, wear of a part of a device can cause the failure of the device as a whole. In addition, as we have proceeded, we have characterized a number of words found in a set of target texts, as it has become possible.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "INTRODUCTION", "sec_num": "1." }, { "text": "We are encoding the knowledge as axioms in what is for the most part a first-order logic, described by Hobbs (1985a) , although quantification over predicates is sometimes convenient. In the formalism there is a nominalization operator ..... for reifying events and conditions, as expressed in the following axiom schema:", "cite_spans": [ { "start": 103, "end": 116, "text": "Hobbs (1985a)", "ref_id": "BIBREF9" } ], "ref_spans": [], "eq_spans": [], "section": "INTRODUCTION", "sec_num": "1." }, { "text": "(Vx)p(x) =-(3e)p'(e,x) A Exist(e)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "INTRODUCTION", "sec_num": "1." }, { "text": "That is, p is true of x if and only if there is a condition e ofp's being true ofx and e exists in the real world.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "INTRODUCTION", "sec_num": "1." }, { "text": "In our implementation so far, we have been proving simple theorems from our axioms using the CG5 theorem-prover developed by Mark Stickel (1982) , and we are now beginning to use the knowledge base in text processing.", "cite_spans": [ { "start": 130, "end": 144, "text": "Stickel (1982)", "ref_id": "BIBREF21" } ], "ref_spans": [], "eq_spans": [], "section": "INTRODUCTION", "sec_num": "1." }, { "text": "There is a notational convention used below that deserves some explanation. It has frequently been noted that relational words in natural language can take only certain types of words as their arguments. These are usually described as selectional constraints. The same is true of predicates in our knowledge base. The constraints are expressed below by rules of the form p(x,y) : r (x,y) This means that for p even to make sense applied to x and y, it must be the case that r is true of x and y. The logical import of this rule is that wherever there is an axiom of the form", "cite_spans": [ { "start": 382, "end": 387, "text": "(x,y)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "REQUIREMENTS ON ARGUMENTS OF PREDICATES", "sec_num": "2" }, { "text": "(V x,y)p(x,y) D q(x,y)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "REQUIREMENTS ON ARGUMENTS OF PREDICATES", "sec_num": "2" }, { "text": "this is really to be read as", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "REQUIREMENTS ON ARGUMENTS OF PREDICATES", "sec_num": "2" }, { "text": "(V x,y)p(x,y) /% r(x,y) ~ q(x,y)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "REQUIREMENTS ON ARGUMENTS OF PREDICATES", "sec_num": "2" }, { "text": "The checking of selectional constraints, therefore, emerges as a by-product of other logical operations: the constraint r(x,y) must be verified if anything else is to be proved from p(x,y).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "REQUIREMENTS ON ARGUMENTS OF PREDICATES", "sec_num": "2" }, { "text": "The simplest example of such an r(x,y) is a conjunction of sort constraints rl(x)/% r2(y). Our approach is a generalization of this, because much more complex requirements can be placed on the arguments. Consider, for example, the verb \"range\". Ifx ranges from y to z, there must be a scale s that includes y and z, and x must be a set of entities that are located at various places on the scale. This can be represented as follows:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "REQUIREMENTS ON ARGUMENTS OF PREDICATES", "sec_num": "2" }, { "text": "range(x,y,z) : (3 s) [scale(s)/% y E s/% z E s/% set(x) /% (V u)[u ~ x D (3 v) v E s/% at(u,v)]]", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "REQUIREMENTS ON ARGUMENTS OF PREDICATES", "sec_num": "2" }, { "text": "3 THE KNOWLEDGE BASE", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "REQUIREMENTS ON ARGUMENTS OF PREDICATES", "sec_num": "2" }, { "text": "At the foundation of the knowledge base is an axiomatization of set theory. It follows the standard Zermelo-Fraenkel approach, except that there is no axiom of infinity.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "SETS AND GRANULARITY", "sec_num": "3.1" }, { "text": "Since so many concepts used in discourse are graindependent, a theory of granularity is also fundamental (see Hobbs 1985b) . A grain is defined in terms of an indistinguishability relation, which is reflexive and symmetric, but not necessarily transitive. One grain can be a refinement of another, with the obvious definition. The most refined grain is the identity grain, i.e., the one in which every two distinct elements are distinguishable. One possible relationship between two grains, one of which is a refinement of the other, is what we call an \"Archimedean relation\", after the Archimedean property of real numbers. Intuitively, if enough events occur that are imperceptible at the coarser grain g2 but perceptible at the finer grain g~, the aggregate will eventually be perceptible at the coarser grain. This is an important property in phenomena subject to the heap paradox. Wear, for instance, eventually has significant consequences.", "cite_spans": [ { "start": 110, "end": 122, "text": "Hobbs 1985b)", "ref_id": "BIBREF10" } ], "ref_spans": [], "eq_spans": [], "section": "SETS AND GRANULARITY", "sec_num": "3.1" }, { "text": "A great many of the most common words in English have scales as their subject matter. This includes many prepositions, the most common adverbs, comparatives, and many abstract verbs. When spatial vocabulary is used metaphorically, it is generally the scalar aspect Of space that carries over to the target domain. A scale is defined as a set of elements, together with a partial ordering and a granularity (or an indistinguishability relation). The partial ordering and the indistinguishability relation are consistent with each other:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "SCALES", "sec_num": "3.2" }, { "text": "(Vx,y,z) x < y A y ~ z D x < zV x ~ z", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "SCALES", "sec_num": "3.2" }, { "text": "That is, ifx is less than y and y is indistinguishable from z, then either x is less than z or x is indistinguishable from z. It is useful to have an adjacency relation between points on a scale, and there are a number of ways we could introduce it. We could simply take it to be primitive; in a scale having a distance function, we could define two points to be adjacent when the distance between them is less than some E; finally, we could define adjacency in terms of the grain size for the scale:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "SCALES", "sec_num": "3.2" }, { "text": "(V x,y,s) adj(x,y,s) =- (3z) Z -s X /% Z -s y /% ~ [x -s Y],", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "SCALES", "sec_num": "3.2" }, { "text": "That is, distinguishable elements x and y are adjacent on scale s if and only if there is an element z which is indistinguishable from both.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "SCALES", "sec_num": "3.2" }, { "text": "Two important possible properties of scales are connectedness and denseness. We can say that two elements of a scale are connected by a chain of adj relations:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "SCALES", "sec_num": "3.2" }, { "text": "(Vx,y,s)connected(x,y,s) - adj(x,y,s) V (3z)adj(x,z,s) /% connected(z,y,s)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "SCALES", "sec_num": "3.2" }, { "text": "A scale is connected (sconnected) if all pairs of elements are connected. A scale is dense if between any two points there is a third point, until the two points are so close together that the grain size no longer allows us to determine whether such an intermediate point exists.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "SCALES", "sec_num": "3.2" }, { "text": "Cranking up the magnification could well resolve the continuous space into a discrete set, as objects into atoms.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "SCALES", "sec_num": "3.2" }, { "text": "(Vs)dense(s) =- (Vx,y)x E s /% y E s /% x --d~, it ceases being topologically invariant, and at a force of strength d 3 ~ d 2, it simply breaks. Metals exhibit the full range of possibilities, that is, 0 < d~ < d2 < d3 < oo. For forces of strength d < d~, the material is \"hard\"; for forces of strength d where d~ < d < d2, it is \"flexible\"; for forces of strength d where d2 < d < d3, it is \"malleable\". Words such as \"ductile\" and \"elastic\" can be defined in terms of this vocabulary, together with predicates about the geometry of the bit of material. Words such as \"brittle\" (dl = d2 = d3) and \"fluid\" (d2 = 0, d3 = oo) can also be defined in these terms. While we should not expect to be able to define various material terms, like \"metal\" and \"ceramic\", we can certainly characterize many of their properties with this vocabulary.", "cite_spans": [ { "start": 175, "end": 187, "text": "Hager (1985)", "ref_id": "BIBREF4" } ], "ref_spans": [], "eq_spans": [], "section": "MATERIAL", "sec_num": "3.5" }, { "text": "Because of its invariance properties, material interacts with containment and motion. The word \"clog\" illustrates this. The predicate clog is a three-place relation: x clogs y against the flow of z. It is the obstruction by x of z's motion through y, but with the selectional restriction that z must be something that can flow, such as a liquid, gas, or powder. If a rope is passing through a hole in a board, and a knot in the rope prevents it from going through, we do not say that the hole is clogged. On the other hand, there do not seem to be any selectional constraints on x. In particular, x can be identical with z: glue, sand, or molasses can clog a passageway against its own flow. We can speak of clogging where the obstruction of flow is not complete, but it must be thought of as \"nearly\" complete.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "MATERIAL", "sec_num": "3.5" }, { "text": "3.6 OTHER DOMAINS 3.6.1 CAUSAL CONNECTION Attachment within materials is one variety of causal connection. In general, if two entities x and y are causally connected with respect to some behavior p of x, then whenever p happens to x, there is some corresponding behavior q that happens to y. In the case of attachment, p and q are both move. A particularly common kind of causal connection between two entities is one mediated by the motion of a third entity from one to the other. (This might be called a \"vector boson\" connection.) Photons mediating the connection between the sun and our eyes, raindrops connecting a state of the clouds with the wetness of our skin and clothes, a virus being transmitted from one person to another, and utterances passing between people are all examples of such causal connections. Barriers, openings, and penetration are all defined with respect to paths of causal connection.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "MATERIAL", "sec_num": "3.5" }, { "text": "The concept of \"force\" is axiomatized, in a way consistent with Talmy's treatment (1985) , in terms of the predications force (a,b,dO and resist(b,a,d2 ) ~ a forces against b with strength dl and b resists a's action with strength d2. We can infer motion from facts about relative strength. This treatment can also be specialized to Newtonian force, where we have not merely movement, but acceleration. In addition, in spaces in which orientation is defined, forces can have an orientation, and a version of the \"parallelogram of forces\" law can be encoded. Finally, force interacts with shape in ways characterized by words like \"stretch\", \"compress\", \"bend\", \"twist\", and \"shear\".", "cite_spans": [ { "start": 64, "end": 88, "text": "Talmy's treatment (1985)", "ref_id": null }, { "start": 126, "end": 151, "text": "(a,b,dO and resist(b,a,d2", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "FORCE", "sec_num": "3.6.2" }, { "text": "An important concept is the notion of a \"system\", which is a set of entities, a set of their properties, and a set of relations among them. A common kind of system is one in which the entities are events and conditions and the relations are causal and enabling relations. A mechanical device can be described as such a system in a sense, in terms of the plan it executes in its operation. The function of various parts and of conditions of those parts is then the role they play in this system, or plan.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "SYSTEMS AND FUNCTIONALITY", "sec_num": "3.6.3" }, { "text": "The intransitive sense of \"operate\", as in", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "SYSTEMS AND FUNCTIONALITY", "sec_num": "3.6.3" }, { "text": "The diesel was operating.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "SYSTEMS AND FUNCTIONALITY", "sec_num": "3.6.3" }, { "text": "involves systems and functionality. If an entity x operates, there must be a larger system s of which x is a part.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "SYSTEMS AND FUNCTIONALITY", "sec_num": "3.6.3" }, { "text": "The entity x itself is a system with parts. These parts undergo normative state changes, thereby causing x to undergo normative state changes, thereby causing x to produce an effect with a normative function in the larger system s. The concept of \"normative\" is discussed below.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "SYSTEMS AND FUNCTIONALITY", "sec_num": "3.6.3" }, { "text": "We have been approaching the problem of characterizing shape from a number of different angles. The classical treatment of shape is via the notion of \"similarity\" in Euclidean geometry, and in Hilbert's formal reconstruction of Euclidean geometry (Hilbert, 1902) the key primitive concept seems to be that of \"congruent angles\". Therefore, we first sought to develop a theory of \"orientation\". The shape of an object can then be characterized in terms of changes in orientation of a tangent as one moves about on the surface of the object, as is done in some vision research (e.g., Zahn and Roskies, 1972) . In all of this, since \"shape\" can be used loosely and metaphorically, one question we are asking is whether some minimal, abstract structure can be found in which the notion of \"shape\" makes sense. Consider, for instance, a graph in which one scale is discrete, or even unordered. Accordingly, we have been examining a number of examples, asking when it seems right to say two structures have different shapes.", "cite_spans": [ { "start": 247, "end": 262, "text": "(Hilbert, 1902)", "ref_id": "BIBREF7" }, { "start": 582, "end": 605, "text": "Zahn and Roskies, 1972)", "ref_id": "BIBREF24" } ], "ref_spans": [], "eq_spans": [], "section": "SHAPE", "sec_num": "3.6.4" }, { "text": "We have also examined the interactions of shape and functionality (see Davis, 1984) . What seems to be crucial is how the shape of an obstacle constrains the motion of a substance or of an object of a particular shape (see Shoham, 1985) . Thus, a funnel concentrates the flow of a liquid, and similarly, a wedge concentrates force. A box pushed against a ridge in the floor will topple, and a rotating wheel is a limiting case of continuous toppling.", "cite_spans": [ { "start": 71, "end": 83, "text": "Davis, 1984)", "ref_id": "BIBREF3" }, { "start": 223, "end": 236, "text": "Shoham, 1985)", "ref_id": "BIBREF20" } ], "ref_spans": [], "eq_spans": [], "section": "SHAPE", "sec_num": "3.6.4" }, { "text": "3.7 HITTING, ABRASION, WEAR, AND RELATED CONCEPTS For x to hit y is for x to move into contact with y with some force. The basic scenario for an abrasive event is that there is an impinging bit of material m that hits an object 0 and by doing so removes a pointlike bit of material bo from the surface of o:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "SHAPE", "sec_num": "3.6.4" }, { "text": "abr-event '(e,m,o,bo) ", "cite_spans": [ { "start": 10, "end": 21, "text": "'(e,m,o,bo)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "SHAPE", "sec_num": "3.6.4" }, { "text": "A (Vt) at(e,t) D topologically-invariant(o,t) m,o, bo)abr-event'(e,m,o,bo) =-(3 t,b,s,ez,e2,e3) at(e,t) A consists-of (o,b,t) A surface(s,b) A particle(bo,s ) A change '(e,el,e 2) A attached'(el,bo,b ) A not'(ez,e 0 A cause(es,e ) A hit '(e3,m,bo) That is, e is an abrasive event of a material m impinging on a topologically invariant object 0 and detaching bo if and only if b 0 is a particle of the surface s of the bit of material material b of which 0 consists at the time t at which e occurs, and e is a change from the condition el of bo's being attached to b to the negation e 2 of that condition, where the change is caused by the hitting e 3 of m against b o.", "cite_spans": [ { "start": 46, "end": 95, "text": "m,o, bo)abr-event'(e,m,o,bo) =-(3 t,b,s,ez,e2,e3)", "ref_id": null }, { "start": 118, "end": 125, "text": "(o,b,t)", "ref_id": null }, { "start": 168, "end": 179, "text": "'(e,el,e 2)", "ref_id": null }, { "start": 237, "end": 247, "text": "'(e3,m,bo)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": ": material(m )", "sec_num": null }, { "text": "(V e,", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": ": material(m )", "sec_num": null }, { "text": "After the abrasive event, the pointlike bit bo is no longer a part of the object o:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": ": material(m )", "sec_num": null }, { "text": "(Ve, m, o, b 0 , e t, e2, tz)abr-e vent '(e, m, o, b o) A change'(e,e Z,ez) A at(e2,t2) A consists-ojffo, b2,t2) D ~ part (bo,b2) That is, if e is an abrasive event of m impinging against 0 and detaching bo, and e is a change from e~ to e2, and e2 holds at time tz, then b 0 is not part of the bit of material b 2 of which 0 consists at t 2. It is necessary to state this explicitly since objects and bits of material can be discontinuous.", "cite_spans": [ { "start": 40, "end": 55, "text": "'(e, m, o, b o)", "ref_id": null }, { "start": 122, "end": 129, "text": "(bo,b2)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": ": material(m )", "sec_num": null }, { "text": "An abrasion is a large set of abrasive events widely distributed through some nonpointlike region on the surface of an object: Wear can result from a large collection of abrasive events distributed over time as well as space (so that there may be no instant at which enough abrasive events occur to count as an abrasion). Thus, the link between wear and abrasion is via the common notion of abrasive events, not via a definition of wear in terms of abrasion. We have not yet characterized the concept \"large\", but we anticipate that it would be similar to \"high\". The concept \"widely distributed\" concerns systems. If x is distributed in y, then y is a system and x is a set of entities which are located at components of y. For the distribution to be wide, most of the elements of a partition of y, determined independently of the distribution, must contain components which have elements of x at them.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": ": material(m )", "sec_num": null }, { "text": "(V", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": ": material(m )", "sec_num": null }, { "text": "(V", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": ": material(m )", "sec_num": null }, { "text": "The word \"wear\" is one of a large class of other events involving cumulative, gradual loss of material w events described by words like \"chip\", \"corrode\", \"file\", \"erode\", \"sand\", \"grind\", \"weather\", \"rust\", \"tarnish\", \"eat away\", \"rot\", and \"decay\". All of these lexical items can now be defined as variations on the definition of \"wear\", since we have built up the axiomatizations underlying \"wear\". We are now in a position to characterize the entire class. We will illustrate this by defining two different types of variants of \"wear\"--\"chip\" and \"corrode\". \"Chip\" differs from \"wear\" in three ways: the bit of material removed in one abrasive event is larger (it need not be point-like), it need not happen because of a material hitting against the object, and \"chip\" does not require (though it does permit) a large collection of such events: one can say that some object is chipped even if there is one chip in it. Thus, we slightly alter the definition of abr-event to accommodate these changes: e,m,o ,bo)chip ' ( e ,m,o, bo) -~ (3t, b,s, el,e2,e3) at(e,t ) A consists-of(o,b,t) /~ surface(s,b) /~ part (bo,s) /~ change'(e,el,ez) /~ attached'(el,bo,b) /~ not'(e2,e O That is, e is a chipping event by a material m of a bit of material bo from an object o if and only if bo is a part of the surface s of the bit of material material b of which o consists at the time t at which e occurs, and e is a change from the condition el of bo's being attached to b to the negation e2 of that condition. \"Corrode\" differs from \"wear\" in that the bit of material is chemically transformed as well as being detached by the contact event; in fact, in some way the chemical transformation causes the detachment. This can be captured by adding a condition to the abrasive event that renders it a (single) corrode event: That is, e is a corrosive event by a fluid m of a bit of material bo with which it is in contact if and only if b 0 is a particle of the surface s of the bit of material b of which 0 consists at the time t at which e occurs, and e is a change from the condition e~ of bo's being attached to b to the negation e 2 of that condition, where the change is caused by a chemical reaction e 3 of m with bo. \"Corrode\" itself may be defined in a parallel fashion to \"wear\", by substituting corrode-event for abr-event.", "cite_spans": [ { "start": 1004, "end": 1057, "text": "e,m,o ,bo)chip ' ( e ,m,o, bo) -~ (3t, b,s, el,e2,e3)", "ref_id": null }, { "start": 1112, "end": 1175, "text": "(bo,s) /~ change'(e,el,ez) /~ attached'(el,bo,b) /~ not'(e2,e O", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": ": material(m )", "sec_num": null }, { "text": "(V", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": ": material(m )", "sec_num": null }, { "text": "All of this suggests the generalization that abrasive events, chipping and corrode events all detach the bit in question, and that we may describe all of these as detaching events. We can then generalize the above axiom about abrasive events that result in loss of material to the following axiom about detaching: m,o,bo,el,e2,t2) detach '(e,m,o,bo) /~ change'(e,el,e2) /~ at(e2,t 2) /~ consists-of(o,t2,b 2) D --7 part (bo,b2) That is, if e is a detaching event by m of b 0 from o, and e is a change from e I to e 2, and e 2 holds at time t2, then bo is not part of the bit of material b 2 of which o consists at t2.", "cite_spans": [ { "start": 314, "end": 330, "text": "m,o,bo,el,e2,t2)", "ref_id": null }, { "start": 338, "end": 349, "text": "'(e,m,o,bo)", "ref_id": null }, { "start": 420, "end": 427, "text": "(bo,b2)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": ": material(m )", "sec_num": null }, { "text": "(V e,", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": ": material(m )", "sec_num": null }, { "text": "Many of the concepts we are investigating have driven us inexorably to the problems of what is meant by \"relevant\" and by \"normative\". We do not pretend to have solved these problems. But for each of these concepts we do have the beginnings of an account that can play a role in analysis, if not yet in implementation.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "RELEVANCE AND THE NORMATIVE", "sec_num": "4" }, { "text": "Our view of relevance, briefly stated, is that something is relevant to some goal if it is a part of a plan to achieve that goal. (A formal treatment of a similar view is given in Davies, forthcoming.) We can illustrate this with an example involving the word \"sample\". If a bit of material x is a sample of another bit of material y, then x is a part of y, and moreover, there are relevant properties p and q such that it is believed that ifp is true ofx then q is true ofy. That is, looking at the properties of the sample tells us something important about the properties of the whole. Frequently, p and q are the same property. In our target texts, the following sentence occurs:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "RELEVANCE AND THE NORMATIVE", "sec_num": "4" }, { "text": "We retained an oil sample for future inspection.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "RELEVANCE AND THE NORMATIVE", "sec_num": "4" }, { "text": "The oil in the sample is a part of the total lube oil in the lube oil system, and it is believed that a property of the sample, such as \"contaminated with metal particles\", will be true of all the lube oil as well, and that this will provide information about possible wear on the bearings. It is therefore relevant to the goal of maintaining the machinery in good working order.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "RELEVANCE AND THE NORMATIVE", "sec_num": "4" }, { "text": "We have arrived at the following provisional account of what it means to be \"normative\". For an entity to exhibit a normative condition or behavior, it must first of all be a component of a larger system. This system has structure in the form of relations among its components. A pattern is a property of the system, namely, the property of a subset of these stuctural relations holding. A norm is a pattern established either by conventional stipulation or by statistical regularity. An entity behaves in a normative fashion if it is a component of a system and instantiates a norm within that system. The word \"operate\", discussed in Section 3.6.3, illustrates this. When we say that an engine is operating, we have in mind a larger system --i.e., the device the engine drives --to which the engine may bear various possible relations. A subset of these relations is stipulated to be the norm --the way it is supposed to work. We say it is operating when it is instantiating this norm.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "RELEVANCE AND THE NORMATIVE", "sec_num": "4" }, { "text": "The research we have been engaged in has forced us to explicate a complex set of commonsense concepts. Since we have done it in as general a fashion as possible, we expect to be able, building on this foundation, to axiomatize a large number of other areas, including areas unrelated to mechanical devices. The very fact that we have been able to characterize words as diverse as \"range\", \"immediately\", \"brittle\", \"operate\", and \"wear\" shows the promising nature of this approach.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "CONCLUSION", "sec_num": "5" }, { "text": "Computational Linguistics Volume 13, Numbers 3-4, July-December 1987", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "", "sec_num": null } ], "back_matter": [ { "text": "The research reported here was funded by the Defense Advanced Research Projects Agency under Office of Naval Research contract N00014-85-C-0013. It builds ", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "ACKNOWLEDGEMENTS", "sec_num": null } ], "bib_entries": { "BIBREF0": { "ref_id": "b0", "title": "A Model of Naive Temporal Reasoning", "authors": [ { "first": "James", "middle": [ "F" ], "last": "Allen", "suffix": "" }, { "first": "Henry", "middle": [ "A" ], "last": "Kautz", "suffix": "" } ], "year": 1985, "venue": "Formal Theories of the Commonsense World", "volume": "", "issue": "", "pages": "251--268", "other_ids": {}, "num": null, "urls": [], "raw_text": "Allen, James F., and Henry A. Kautz. 1985. A Model of Naive Temporal Reasoning. In: Jerry R. Hobbs and Robert C. 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IEEE Transactions on Computers, Vol. C-21, No. 3: 269-281.", "links": null } }, "ref_entries": { "FIGREF0": { "type_str": "figure", "text": ")space(sp) =-(:lSl,S2) scalel(sl,sP) A scale2(s2,sp)", "uris": null, "num": null }, "FIGREF1": { "type_str": "figure", "text": "e,m,o) abrade'(e,m,o) =-- (3 bs)large(bs)A[(Vet)[e I E e D (:1 bo)b 0 E bs A abr-event'(et,m,o,bo) ] A(Vb,s,t)[at(e,t) A consists-of(o,b,t) A surface(s,b) D (3r) subregion(r,s) A widely-distributed(bs,r)]] That is, e is an abrasion by m of o if and only if there is a large set bs of bits of material and e is a set of abrasive events in which m impinges on o and removes a bit bo, an element in bs, from o, and if e occurs at time t and o consists of material b at time t, then there is a subregion r of the surface s of b over which bs is widely distributed.", "uris": null, "num": null }, "FIGREF2": { "type_str": "figure", "text": "e,m,o) wear'(e,m,o) --(3bs) large(bs) A [(Vet)[e t E e D (3 bo)b o ~ bs A abr-event'(e l,m,o,bo)] A (3i)[interval(i) A widely-distributed(e,i)]] That is, e is a wearing by x of o if and only if there is a large set bs of bits of material and e is a set of abrasive events in which m impinges on o and removes a bit bo, an element in bs, from o, and e is widely distributed over some time interval i.", "uris": null, "num": null }, "FIGREF3": { "type_str": "figure", "text": "corrode-event(m, o, b o) : fluid(m) /~ contact(m,b o) (V e,m,o,b o) corrode-event'(e,m,o,bo) =--(3 t,b,s,el,e2,e 3) at(e,t) /~ consists-of(o,b,t) /~ surface(s,b) /~ particle(bo,s) /~ change'(e,ei,e 2) /~ attached'(el,bo,b) /~ not'(e2,e 0/~ cause(ea,e) /~ chemical-change'(e3,m,b o)", "uris": null, "num": null } } } }