{ "paper_id": "C82-1003", "header": { "generated_with": "S2ORC 1.0.0", "date_generated": "2023-01-19T13:13:26.455461Z" }, "title": "KNOWLEDGE REPRESENTATION METHOD BASED ON pREDICATE CALCULUS IN AN INTELLIGENT CAI SYSTEM", "authors": [ { "first": "Barbara", "middle": [], "last": "Belier", "suffix": "", "affiliation": { "laboratory": "", "institution": "University of Pozna~", "location": { "country": "Poland" } }, "email": "" } ], "year": "", "venue": null, "identifiers": {}, "abstract": "The knowledge representation method is introduced to be applied in the ICAI system to teach prog~-min~ language\u00b0 Knowledge about syntax and semanties of that language is represented by a set of axioms w~itten in the predicate calculus language, The directed graph of concepts is mentioned as a method to represent an instr~ctlonal structure of the domain knowledge. The pros[ procedure to answer student's questions is described.", "pdf_parse": { "paper_id": "C82-1003", "_pdf_hash": "", "abstract": [ { "text": "The knowledge representation method is introduced to be applied in the ICAI system to teach prog~-min~ language\u00b0 Knowledge about syntax and semanties of that language is represented by a set of axioms w~itten in the predicate calculus language, The directed graph of concepts is mentioned as a method to represent an instr~ctlonal structure of the domain knowledge. The pros[ procedure to answer student's questions is described.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Abstract", "sec_num": null } ], "body_text": [ { "text": "The early 70S have brouF~at the Intelligent CAI /ICAI/ systems [3~4~o In these systems all course material is represented independently of teachin~ procedures. The goal of ICAI research is to obtain an individualization of inst1~aotion by providin~ an ability of answerln~ studentts questions as well as genel~atin~ remedial oomments~problems and advioes~ aeco1~Lin~ly to current studentPs respormos and his abilities and preferences in general.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "INTRODUCTION", "sec_num": null }, { "text": "ICAI researchers have firstly focused their investigations on representation of the subject matter. Mostly semantic nets have been used as representation of static [~J and procedural [~p~] domain knowled-Ge. Database of an instz~ctlo~Ll system includes also a representation of currlculumto or~nlze an instz~uotlon of new knowledge [~pY~ It is helpful in seleotln~ material to be presented to the student.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "INTRODUCTION", "sec_num": null }, { "text": "the knowledge representation method based on predicate calculus in an intelligent C AT system~ which is applied to teach the programmi~ language [J] o The prototype of the presented approach w~s an application of predloate calculus to describe pro~ramsp written in ALGOL~ to l~ove their oozTe\u00a9tness~ introduced by ~stall [2] . The ~aowledge about syntu and semantlos of\" the prog-rmmni~ lan6~a~e has been represented in the form of a set of first oz~er logic axloms~ -ability to express a large set of concepts of the domain bein~ \u2022 taught p -facility of codln~ these concepts and relations amon~ them~ -easy way to t~ansform the formal notation into the natur~l language formp -effiolenoy of information retrieval duri~ the process of ans-werin~ user's query and proving the correctness of his answer~ -ability of automated deduction application in the question -answerln~ process.", "cite_spans": [ { "start": 145, "end": 148, "text": "[J]", "ref_id": null }, { "start": 321, "end": 324, "text": "[2]", "ref_id": "BIBREF1" } ], "ref_spans": [], "eq_spans": [], "section": "Th\u00a3s paper presents", "sec_num": null }, { "text": "Let us conside~ a subset of an ALGOL-llke progx~ammin~ lan~uage~con-tainin~ simple arithmetic and logical expressions~ instruction of substitution and conditional and o~ instructions. We assume that each instruction has been written in a separate line of program.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Th\u00a3s paper presents", "sec_num": null }, { "text": "The predicate calculus language developed to represent knowledge about the progI~ammlng lan6~age contains:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Th\u00a3s paper presents", "sec_num": null }, { "text": "-names of sets~ called sorts of objects~ representing elements of syntax and semantics of a pro~Tammln~ lan~uagep -funotions~ transformln~ obJeotsp -predioates~ representin~ relations between objects. Some sortsj functions and predicates are introduced to represent syntax of the prog~ammlng lan~uage.0thers represent its semantics. N o t a t i o n. The ordinary predicate calculus notation has been used. Some modifications improve the readability of statements:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Th\u00a3s paper presents", "sec_num": null }, { "text": "-unquantified vat-fables are gener~lly qua~t~.~le~. ~ -two-places predicates are written in an infix manner~ binary arithmetic functions are written in an infix ma~n~rp -parenthesis are used in the ordinary meanin~ -clauses are separated by dots.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Th\u00a3s paper presents", "sec_num": null }, { "text": "s y n t a x. The program syntax has been described by a set of clauses w~itten in the predicate calculus language. Sorts of objects /examples/~ identifier~ number~ expresslon~ arlthmetio expression~ logical expression~ label~ instruction~ program line.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "P r o g r a m", "sec_num": null }, { "text": "Functions transform some expressions_into te~ms~ by example:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "P r o g r a m", "sec_num": null }, { "text": "dod_~ wax wa-w-wa where: ~a -arithmetic expression~ it: wa~wa---wl wl -logical expression~ pod_~ id x wy~ in id -identifier~ sko; et~ in wy -expression~ et -label~ ifl: wl \u00d7 wi ----in in -instruction~ ~ri -program line. First of these functions constructs an expression~ which represents an operation of addition~ the second one gives as a result an expression representing the \"less than\" relation and the others cons-tr~et appropriately the substitution instr~ction~ the ~ instruction and the conditional instruction.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "P r o g r a m", "sec_num": null }, { "text": "wins ~wix in pet ~ et ~ wi ~s ~ wl x wi First of these predicates indicates the location of an instruction in a given pro~z~m llne r the second one assi~s a label at the be-6~i~ning of a progmam line and the third one determines the direct succession of two progx~um lines in a sequence.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Some p~edlcates have been introduced to represent the syntax relations between syntax obJeots~ like followin~:", "sec_num": null }, { "text": "Example,. The syntax of a pro~am containing three followin~ substi-~uti one : Predicates assign states to iooatior~ in a program: stwe c-st ~wi stzm ~st \u00d7wi Pirs$,c~\" them associates a state to a program line before an execution of an instruction from this lineo The second one indicateo 9 that the control p~ssee ~o an instruction ~ri%ten in a ~iven program line in a ~iven state. ", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Some p~edlcates have been introduced to represent the syntax relations between syntax obJeots~ like followin~:", "sec_num": null }, { "text": "J = L L= L+ 2 E- K = J + L", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Some p~edlcates have been introduced to represent the syntax relations between syntax obJeots~ like followin~:", "sec_num": null }, { "text": "An assumption is done that all knowledge to be tau6ht can be divided to instructional units.Thus the first step to oonstr~ot an instructional structure representation is to select such units /concepts/. Each of them has a name and at least one sentence can be told about it /unreal concepts are not allowed/.Some introductory concepts are assumed to be known to the student. The next step is to specify all relations between concepts.These relations could be:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "DIRECTED GRAPH AS A D~rHOD OF INSTRUCTIONAL STRUCTURE REPRESENTATION", "sec_num": null }, { "text": "/a/ Concept X is a part of Y, /b/ Concept X has a property~ represented by Z~ ~ oncept X is a reason Or a Justification of T, Concept X belongs to the object class represented by K, /e/ Concept X is an alternative of A~ /f/ Concept X is equivalent to W at least in some circumstances.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "DIRECTED GRAPH AS A D~rHOD OF INSTRUCTIONAL STRUCTURE REPRESENTATION", "sec_num": null }, { "text": "Each relation corresponds with a graph, which nodes represent concepts from an introduced set of concepts.The composition of all obtained 6~aphs rerults in a final graph~whlch represents an instructional structure of the subject matter.Because of the different interpretation of the particular arches of this ~Taph /which are described by various relationships/ the \"superior-inferior\" relation is introduced as the universal one which represents every relation between concepts.Thus the dlrested ~phhas been obtained,~ith arrows directed to the superior concepts.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "DIRECTED GRAPH AS A D~rHOD OF INSTRUCTIONAL STRUCTURE REPRESENTATION", "sec_num": null }, { "text": "A set of axioms is associated with each node of the concept graph. Also some other information may be associated with it.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "DIRECTED GRAPH AS A D~rHOD OF INSTRUCTIONAL STRUCTURE REPRESENTATION", "sec_num": null }, { "text": "The followin~ problems have to be solved| -choice and specifyin~ of classes of user's queries,which can be answered by the ICAI system~ -reco@~nition of a main subject of the query, translation of the query from natural language to the predicate calculus language formula, -application of the automated theorem-provin~ techniques to retrieve an answer, -generatin~ of an answer in natura~ language form.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "ANSWERING STUDENT'S QUESTIONS", "sec_num": null }, { "text": "Three classes of queries have been qonsidered: /I/ Decision queries of gener~l\\form in natural language < sentence> 7 where: /existin~ in Polish/ determines that a question belongs to this class 9 ~entenoe> -indicative sentence,", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "ANSWERING STUDENT'S QUESTIONS", "sec_num": null }, { "text": "which require an answer in the form .Y~s, or \"No\". whloh can be t~sfo .treed into the form: Which Z eatlsfies: Z~ ~clause> ? /b/ What is implied by ~elause> ? which can be tz~nsfo~med into the formz Which Z satisfies = ~olause~Z ? In the above problem queries: Z -the clause to be found t ~olause~ -clause obta/ned from the tx~nslate~ query. P~oblem queries ~equlre an answer in the foz~ of a senten-COo An analysis Of a userts quex-y should flx the main subject of it in the terms of a subset of conoepts~represented on the concept g~ph.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "ANSWERING STUDENT'S QUESTIONS", "sec_num": null }, { "text": "A dofiD/tlon of acceptable language of user's queries involves the form of translation rules from n~tux~tl lan~u.age into the predloate calculus formula. It is worth notloln~ that:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "ANSWERING STUDENT'S QUESTIONS", "sec_num": null }, { "text": "-querles in the natural lar~ua~e \u00a3orm have the threefold nature~ it means they can be counted into the three mentioned above olasses~ -queries fragments in the form of indicative clauses are built from expressed in natural language p~edloates~introduee~ in the present ed f or~alization~ -in respect of quantity of expressions the language of user's queries is comparable with the laa1&~e obtained in the process of translation of p~ed/oate calculus axioms into natural lan~ua~e~ -lan@uaGe o~ user's queries and the predloate calculus l~a~e have a common base of basle concepts because the sorts of ob~eots~ functions and pFedicates introduced in the predloate calculus language correspond with some specified natural language expressions.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "ANSWERING STUDENT'S QUESTIONS", "sec_num": null }, { "text": "It has been submitted that questlon-answering problem m~y be solved with an application o~ auto~te~ theorem-pyo~,in~ teohnlques~ namely on the base o[ the resolution principle [8] ,This method~ based only on the s~rnteac of olauses~ doesn't require to control the proo~ procedure by the user,The resolution prlnelple requires to convert all formulas into the Skolem conjunctive form. Thus each formula becomes a set of olauses~ each of them bei~E a dlsjunotion of literals,", "cite_spans": [ { "start": 176, "end": 179, "text": "[8]", "ref_id": "BIBREF7" } ], "ref_spans": [], "eq_spans": [], "section": "ANSWERING STUDENT'S QUESTIONS", "sec_num": null }, { "text": "The question-ans~ering procedure for deolslon queries tries to pro-~e that a negation of formula ~ ob%alned after translation of the qu-er~ is false, I\u00a3 it's so~ an answer is \"Yes\". If a proo~ procedure applied to the formula in its a~firmati~/e ~or~ provides a sucoess~ an answer is \"NO\".Some questions may be unsolvable in the lack of kno~le~e.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "ANSWERING STUDENT'S QUESTIONS", "sec_num": null }, { "text": "The proof procedure \u00a3or objective queries examines a \u00a3ormula", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "ANSWERING STUDENT'S QUESTIONS", "sec_num": null }, { "text": "~~x (w (x} ~ A (x))", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "ANSWERING STUDENT'S QUESTIONS", "sec_num": null }, { "text": "which is supposed to be false.The proof prroedure tries to retrieve a counter-example, if i% exists, which will be substituted in the place of X o I% has been assumed that problem queries are in the implication form after the translation proeess. Question-answerin~ procedure for this class of queries has been reduced to such onetwhich tries to retrieve an answer from one axiom. For the first subclass of problem queries a search is made for an axiom in the implication form, ~hich conclusion embodies the conclusion of the formula obtained from the tx~ansformed query. The premises of this axiom are an answer\u00b0 The proof procedure applied to answer a question of the second subclass tries to find an axiom~ which premises are implied by premises of the formula obtained f~om the transformed query. The conclusion of this axiom is an answer.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "ANSWERING STUDENT'S QUESTIONS", "sec_num": null }, { "text": "The proper way to reduce a number of clauses taking a part in the resolution process is to constr,~ct an initial active set of clauses as a set containing only clauses of axioms concerning concepts reco-~LIzed in the query and clauses of formula obtained from the query. The translation rules,applied to transform axioms from the predicate calculus language into the natural language expressions t can be used also to translate the retrieved answer to the natural language\u00b0 CONCLUSIONS Described above ~1o~le~e", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "ANSWERING STUDENT'S QUESTIONS", "sec_num": null }, { "text": "representatiom method based on predicate calculus has been applied to the large subset of FORTRAN 1900 [I] . I% has been sho~n that this method satisfies criteria required in the ICAI system. An application of the predicate calculus language to describe knowledge about the programming language provides the automated answering of student's questions,whlch is the main advantage of this method.", "cite_spans": [ { "start": 103, "end": 106, "text": "[I]", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "ANSWERING STUDENT'S QUESTIONS", "sec_num": null }, { "text": "T~Lis method is applicable to those domains of ~owledge, which can be represented by the set of first or~er logic axioms, with regard to their formalized nature.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "ANSWERING STUDENT'S QUESTIONS", "sec_num": null } ], "back_matter": [], "bib_entries": { "BIBREF0": { "ref_id": "b0", "title": "~ Method of representation of subject matter in the computer system to teach pro~ammlng lan~ua~e~ Ph.D. Thesis /in Polish/, Reg", "authors": [ { "first": "B", "middle": [], "last": "Begier", "suffix": "" } ], "year": 1980, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Begier B. ~ Method of representation of subject matter in the computer system to teach pro~ammlng lan~ua~e~ Ph.D. Thesis /in Polish/, Reg. Comp. Center, Tech. Univ. of Pozna~ /1980/.", "links": null }, "BIBREF1": { "ref_id": "b1", "title": "~ Formal description of program str~cture and semantics in first order logic", "authors": [ { "first": "R", "middle": [ "M" ], "last": "Burstall", "suffix": "" } ], "year": 1969, "venue": "Math. Intell", "volume": "5", "issue": "", "pages": "79--98", "other_ids": {}, "num": null, "urls": [], "raw_text": "Burstall R.M.~ Formal description of program str~cture and se- mantics in first order logic, Math. Intell. 5 /1969/ 79-98", "links": null }, "BIBREF2": { "ref_id": "b2", "title": "CAI: an artificial intelli~ence approach to computer-assisted instruction", "authors": [ { "first": "J", "middle": [ "R" ], "last": "Carbenell", "suffix": "" }, { "first": "", "middle": [], "last": "Ai", "suffix": "" } ], "year": 1970, "venue": "", "volume": "11", "issue": "", "pages": "190--202", "other_ids": {}, "num": null, "urls": [], "raw_text": "Carbenell J.R.~ AI in CAI: an artificial intelli~ence approach to computer-assisted instruction, IEEE Trans. on Man-Machine Systems 11 /1970/ 190-202", "links": null }, "BIBREF3": { "ref_id": "b3", "title": "~ Appllcations-oriented AI research= education, Rep. STAN-CS-79-749~ Dep", "authors": [ { "first": "W", "middle": [ "J" ], "last": "Clancey", "suffix": "" }, { "first": "J", "middle": [ "S" ], "last": "Be~et", "suffix": "" }, { "first": "J", "middle": [ "R" ], "last": "Cohen", "suffix": "" } ], "year": 1979, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Clancey W.J,, Be~et J.S., Cohen J.R. ~ Appllcations-oriented AI research= education, Rep. STAN-CS-79-749~ Dep. of Comp. So., Stanford Univ. /July 1979/", "links": null }, "BIBREF4": { "ref_id": "b4", "title": "Computer-aided instruction system to t~ch the pro~ammlng language FORTRA~ Rep. of Re~", "authors": [], "year": 1980, "venue": "Compo Centerp Teoh.Unlv.Poznad", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Computer-aided instruction system to t~ch the pro~ammlng lan- guage FORTRA~ Rep. of Re~. Compo Centerp Teoh.Unlv.Poznad /1980/", "links": null }, "BIBREF5": { "ref_id": "b5", "title": "The genetic graph: a representation for the eve. lution of procedural Enowledge", "authors": [ { "first": "I", "middle": [ "P" ], "last": "Goldstein", "suffix": "" } ], "year": 1979, "venue": "Int.J.Man-Machine Studies", "volume": "11", "issue": "", "pages": "51--77", "other_ids": {}, "num": null, "urls": [], "raw_text": "Goldstein I.P. ~ The genetic graph: a representation for the eve. lution of procedural Enowledge, Int.J.Man-Machine Studies 11 /1979/ 51-77", "links": null }, "BIBREF6": { "ref_id": "b6", "title": "Some tho~h% about represen\u00a2ing knowledge in instructional systems~ Fourth Int. 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Intel~., ~ilisi /1975/ 122-125", "links": null }, "BIBREF7": { "ref_id": "b7", "title": "Automated theorem proving= a losical basis /North Holland~ Amsterdam", "authors": [ { "first": "D", "middle": [ "W" ], "last": "Loveland", "suffix": "" } ], "year": null, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Loveland D.W.~ Automated theorem proving= a losical basis /North Holland~ Amsterdam, 19~8 /", "links": null } }, "ref_entries": { "FIGREF0": { "uris": null, "text": "Sorts o~ ob~eets~ functions and predicates are the b~is o~ a ~r~mmar of ~he predicate cal~ulus lang~a~e~ which expreu~ions are ~sed %o repmesent knowl~d~e about %he prosx'anuruin~ lanGu~eo Axioms written ~n this language descx~ibe a~hme%lo 1~les~ propeP~ ties of ex~ressions~ seman%ics of instructions /princlple~ of exe= oution of instr~ctions/~ meaning of program se~nen%c or blocks etOo Ez~unple~ A~ axiom de~oribin~ semantics of a~ ins~muo$ion of substitution: wl ~in~ pod (J~X] s stwe wl A w2 bna____~s wl The premises of this axiom !nelude~ %ho location el\" the ~ubstltutlon J = X in the pro~Tam i~ne~ ~ ~ %he ~ssi~m~ of the s%~%e before an execution o. ~. %~.~is instrue~ion~and a faot~that the program line w2 directly follo~s\"wlo The ooncl~slo~ says~ %.h~ a s~;ate next of s as %he state before an exertion of an instruction written in ~2 and 8 value of the variable J in the state next of s is a value of an exp~-ession X in the ~tate s ~nd ~ ~lue of any variable Y ~ J doesn't ehan~e during %he %rar~fer from the state s to the next of ~o A l~r~e subse~ o\u00a3 FORTRAN has been de$~rlbed in this manner [~] \u00b0 it tul~n8 out ~hat form%11as of p~edicate calculus a~e easy to tr~ns-form into na%~ral la~ e~os\u00a3~. Axles are divided into simple sentences. Translati~ rales are applied to simple sentences. Each object has and me in natur~l l~ge. Also an appropriate ~-%ural language expression is selected for eaohfunotion.Eaah predicate cOrTesponds with a verb phrase in natural language. The proper translation rules for functions and objects sure applied with reference te arguments of a predloate.~lation ~les for Polish language have been reported in [I] as well as their a~plication to all axioms descrlbin~ FORTRAN.", "num": null, "type_str": "figure" }, "FIGREF1": { "uris": null, "text": "Objective quez-lee of ~enez~al foz~ in natuz~l lansuage Whloh ~senex~l name> in the query, A(X) -. formula obtained iron the tz~nslated queryp which describes some prope~ties of X. /3/ Problem quex-ies of general form in natural language", "num": null, "type_str": "figure" } } } }