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Artificial Intelligence Definite clause grammars and semantic interpretation Fall 2008 professor: Luigi Ceccaroni.

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1 Artificial Intelligence Definite clause grammars and semantic interpretation Fall 2008 professor: Luigi Ceccaroni

2 Semantic interpretation The task of determining the meaning of a sentence can be divided into 2 steps: 1.Computing a context-independent notion of meaning (e.g., via DCG parsing) = semantic interpretation 2.Interpreting the parsed sentence in context to produce the final meaning representation Many actual systems do not make this division and use contextual information early in the processing 2

3 What are definite clause grammars? Definite Clause Grammars (DCGs) are convenient ways to represent grammatical relationships for various parsing applications. They can be used for natural language work, for creating formal command and programming languages. Quite simply, they are a nice notation for writing grammars that hides the underlying difference list variables.

4 DCGs A little grammar written as a DCG: s --> np, vp. np --> det, n. vp --> v, np. vp --> v. det --> [the]. det --> [a]. n --> [woman]. n --> [man]. v --> [shoots]. How do we use this DCG? In fact, we use it in exactly the same way as we used the difference list recognizer.

5 DCGs For example, to find out whether a woman shoots a man is a sentence, we pose the query: s([a,woman,shoots,a,man],[]). That is, just as in the difference list recognizer, we ask whether we can get an s by consuming the symbols in [a,woman,shoots,a,man], leaving nothing behind.

6 DCGs Similarly, to generate all the sentences in the grammar, we pose the query: s(X,[]). This asks what values we can give to X, such that we get an s by consuming the symbols in X, leaving nothing behind. Moreover, the queries for other grammatical categories also work the same way. For example, to find out if a woman is a noun phrase we pose the query: np([a,woman],[]).

7 DCGs We generate all the noun phrases in the grammar as follows: np(X,[]). Quite simply, this DCG is a difference list recognizer! That is, DCG notation is essentially syntactic sugar: user friendly notation that lets us write grammars in a natural way.

8 DCGs The Prolog language can translate this notation into the kinds of difference lists discussed before. So we have the best of both worlds: –a nice simple notation for working with –the efficiency of difference lists

9 DCGs To see what Prolog translates DCG rules into: –let Prolog consult the rules of this DCG, then if you pose the query: listing(s) –you will get the response: s(A,B) :- np(A,C), vp(C,B). This is what Prolog has translated s --> np,vp into. Note that this is exactly the difference list rule we used in the recognizer.

10 DCGs Similarly, if you pose the query: listing(np) you will get: np(A,B) :- det(A,C), n(C,B). This is what Prolog has translated np --> det,n into. Again (apart from the choice of variables) this is the difference list rule we used in the recognizer.

11 DCGs To get a complete listing of the translations of all the rules, simply type: listing.

12 Separating rules and lexicon By separating rules and lexicon we mean that we want to eliminate all mentioning of individual words in the DCGs and instead record all the information about individual words separately in a lexicon. To see what is meant by this, let's return to the basic grammar, namely: np - - > det, n. vp - - > v, np. vp - - > v. det - - > [the]. det - - > [a]. n - - > [woman]. n - - > [man]. v - - > [shoots].

13 Separating rules and lexicon We are going to separate the rules form the lexicon. That is, we are going to write a DCG that generates exactly the same language, but in which no rule mentions any individual word. All the information about individual words will be recorded separately.

14 Separating rules and lexicon Here is an example of a (very simple) lexicon. Lexical entries are encoded by using a predicate lex/2 whose first argument is a word, and whose second argument is a syntactic category: lex(the, det). lex(a, det). lex(woman, n). lex(man, n). lex(shoots, v).

15 Separating rules and lexicon A simple grammar that could go with this lexicon will be very similar to the basic DCG. In fact, both grammars generate exactly the same language. The only rules that change are those that mention specific words, i.e. the det, n, and v rules. det --> [Word], {lex(Word, det)}. n --> [Word], {lex(Word, n)}. v --> [Word], {lex(Word, v)}.

16 Separating rules and lexicon Grammar: np - - > det, n. vp - - > v, np. vp - - > v. det --> [Word], {lex(Word, det)}. n --> [Word], {lex(Word, n)}. v --> [Word], {lex(Word, v)}.

17 Separating rules and lexicon Consider the new det rule: det --> [Word], {lex(Word, det)}. This rule says “a det can consist of a list containing a single element Word” (note that Word is a variable). The extra test adds the crucial condition: “as long as Word matches with something that is listed in the lexicon as a determiner”.

18 Separating rules and lexicon With our present lexicon, this means that Word must be matched either with the word “a” or “the”: lex(the, det). lex(a, det). So this single rule replaces the two previous DCG rules for det.

19 Separating rules and lexicon This explains the how of separating rules from lexicon, but it doesn't explain the why. Is it really so important? Is this new way of writing DCGs really that much better?

20 Separating rules and lexicon The answer is yes! for a theoretical reason: –Arguably rules should not mention specific lexical items. –The purpose of rules is to list general syntactic facts, such as the fact that a sentence can be made up of a noun phrase followed by a verb phrase. –The rules for s, np, and vp describe such general syntactic facts, but the old rules for det, n, and v don't. –Instead, the old rules simply list particular facts: that a is a determiner, that the is a determiner, and so on. –From a theoretical perspective it is much neater to have a single rule that says “anything is a determiner (or a noun, or a verb,...) if it is listed as such in the lexicon”.

21 Separating rules and lexicon Now, our little lexicon, with its simple lex entries, is a toy. But a real lexicon is (most emphatically!) not. A real lexicon is likely to be very large (it may contain hundreds of thousands, or even millions, of words) and moreover, the information associated with each word is likely to be very rich.

22 Separating rules and lexicon Our lex entries give only the syntactical category of each word. A real lexicon will give much more, such as information about its phonological, morphological, semantic, and pragmatic properties. Because real lexicons are big and complex, from a software engineering perspective it is best to write simple grammars that have a well-defined way of pulling out the information they need from vast lexicons.

23 Separating rules and lexicon That is, grammars should be thought of as separate entities which can access the information contained in lexicons. We can then use specialized mechanisms for efficiently storing the lexicon and retrieving data from it. The new rules really do just list general syntactic facts, and the extra tests act as an interface to our (admittedly simple) lexicon that lets the rules find exactly the information they need.

24 Grammar 1: a trivial grammar for a fragment of language s  np, vp. % A sentence (s) is a noun phrase (np) plus a verb phrase (vp) np  det, n. % A noun phrase is a determiner plus a noun np  n. %... or just a noun. vp  v, np. % A verb phrase is a verb and its direct object, which is an np vp  v. %... or just the verb (for intransitives). det  [Word], {lex(Word, det)}. n  [Word], {lex(Word, n)}. v  [Word], {lex(Word, v)}.

25 Grammar 1: a trivial grammar for a fragment of language lex(the, det). % ‘the’ is a determiner lex(mary, n).% ‘mary’ is a noun. lex(john, n). lex(woman, n). lex(apple, n). lex(man, n). lex(loves, v).% ‘loves’ is a verb. lex(eats, v). lex(sings, v).

26 Sentences for Grammar 1 mary loves john the woman eats the apple the man sings mary eats

27 Grammar 2: restrictions in argument selection s  np, vp. compl([])  []. compl([arg(X)])  p(X), np. compl([])  np. np  name. np  det, n. vp  v(X), compl(X). % A vp is a verb plus a verbal complement (compl)

28 Grammar 2: restrictions in argument selection v(A)  [Word], {lex(Word, v, A)}. name  [Word], {lex(Word, name)}. n  [Word], {lex(Word, n)}. det  [Word], {lex(Word, det)}. p(Word)  [Word], {lex(Word, p)}.

29 Grammar 2: restrictions in argument selection lex(piensa, v, [arg(en)]). lex(está, v, [arg(en)]). lex(ríe, v, []). lex(habla, v, [arg(con)]). lex(lee, v, []). lex(el, det). % ‘el’ is a determiner

30 Grammar 2: restrictions in argument selection lex(un, det). lex(mary, name). lex(john, name). lex(profesor, n). lex(en, p)

31 Sentences for Grammar 2 mary piensa en john john habla con mary john ríe un profesor habla con mary

32 Extension of Grammar 2 John habla de Clara con Mary Needed modifications: –compl([arg(X) | Y])  p(X), np, compl(Y). –lex(habla, v, [arg(de), arg(con)]). –lex(clara, name).

33 Grammar 3: logical representation of sentences s(F)  np(S), v(S, X, F), compl(X). compl([ ])  [ ]. compl([arg(X,O) | Y])  p(X), np (O), compl(Y). compl([arg(null, O) | Y])  np(O), compl(Y). np(S)  name(S). np(S)  det, n(S).

34 Grammar 3: logical representation of sentences v(S,A,F)  [Word], {lex(Word, v, S, A, F)}. name(Word)  [Word], {lex(Word, name)}. n(Word)  [Word], {lex(Word, n)}. det  [Word], {lex(Word, det)}. p(Word)  [Word], {lex(Word, p)}.

35 Grammar 3: logical representation of sentences lex(clara, name). lex(maria, name). lex(juan, name). lex(barcelona, name). lex(libro, n). lex(hombre, n). lex(profesor, n).

36 Grammar 3: logical representation of sentences lex(el, det). lex(un, det). lex(en, p). lex(con, p). lex(de, p).

37 Grammar 3: logical representation of sentences lex(ríe, v, S, [], reir(S)). lex(piensa, v, S, [arg(en, O)], pensar_en(S, O)). lex(habla, v, S, [arg(de, O),arg(con, O1)], comunica(S,O, O1)). lex(habla, v, S, [arg(con, O),arg(de, O1)], comunica(S,O1, O)). lex(está, v, S, [arg(en, O)], locativo(S, O)). lex(lee, v, S, [arg(null, O)], leer(S, O)).

38 Sentences for Grammar 3 unary predicate (ríe, v, S, [ ], reir(S)). binary predicate (piensa, v, S, [arg(en, O)], pensar_en(S, O)). ternary predicate (habla, v, S, [arg(con,O), arg(de, O1)], comunica(S, O1, O)). Example: –Juan piensa en Maria = pensar_en(juan, maria).

39 Prolog input and output analysis(F, X, [ ]):- s(F, X, [ ]). | ?- analysis(F, [juan, está, en, barcelona], [ ]). F = locativo(juan, barcelona) ? yes | ?- analysis(F, [juan, piensa, en, maria], [ ]). F = pensar_en(juan, maria) ? yes

40 Prolog input and output | ?- analysis(F, [el, libro, está, en, barcelona], [ ]). F = locativo(libro, barcelona) ? yes | ?- analysis(F, [juan, lee, un, libro], [ ]). F = leer(juan, libro) ? yes

41 Prolog input and output | ?- analysis(F, [el, hombre, habla, de, juan, con, maria], [ ]). F = comunica(hombre, juan, maria) ? yes | ?- analysis(F, [el, hombre, ríe], [ ]). F = reir(hombre) ? yes

42 Prolog input and output | ?- analysis(F, [el, profesor, piensa, en, un, libro], [ ]). F = pensar_en(profesor, libro) ? yes

43 Grammar 4: quantification It exists X and X is a libro: –el libro = e(X, libro(X)). All X such that X is a libro: –todo libro = a(X, libro(X)).

44 Grammar 4: quantification el libro cae = e(X, and(libro(X), cae(X))) Juan piensa en el libro = e(X, and(libro(X), piensa(juan, X))) todo hombre piensa en el libro = a(X, implies(hombre(X), e(Y, and(libro(Y), piensa(X,Y)))

45 Grammar 4: quantification lex(el,det,K,S1,S2,e(K,and(S1,S2))). lex(un,det,K,S1,S2,e(K,and(S1,S2))). lex(los,det,K,S1,S2,a(K,implies(S1,S2))). lex(todo,det,K,S1,S2,a(K,implies(S1,S2))). np(K,S2,F)  det(K,S1,S2,F), n(K,S1). np(K,F,F)  name(K).

46 Grammar 4: quantification compl([ ],S,S)  [ ]. compl([arg(X,K) | Y],S1,S)  p(X), np(K,S2,S), compl(Y,S1,S2). s(S)  np(K,S2,S), v(K,X,S1), compl(X,S1,S2). n(K,F)  [Word],{lex(Word,n,K,F)}. lex(libro,n,K,libro(K)).

47 Prolog input and output | ?- analysis(F,[el,hombre,ríe],[ ]). F = e(_A,and(hombre(_A),reir(_A))) ? yes | ?- analysis(F,[el,profesor,piensa,en,un,libro],[ ]). F = e(_B,and(profesor(_B),e(_A,and(libro(_A),pensar_en(_B,_A))))) ? yes

48 Prolog input and output | ?- analysis(F,[el,hombre,habla,de,juan,con,maria],[ ]). F = e(_A,and(hombre(_A),comunica(_A,juan,maria))) ? yes | ?- analysis(F,[todo,hombre,piensa,en,un,libro],[ ]). F = a(_B,implies(hombre(_B),e(_A,and(libro(_A),pensar_en(_B,_A))))) ? yes

49 Prolog input and output | ?- analysis(F,[todo,libro,esta,en,barcelona],[ ]). F = a(_A,implies(libro(_A),locativo(_A,barcelona))) ? yes

50 Extension of Grammar 4 El hombre bueno: –e(X, and(hombre(X), bueno(X)))

51 Grammar 5: semantic constraints Argument selection: –*Juan lee el hombre –El gato come pescado –El perro corre por el camino Semantic categories: –human: Juan, María, Clara, hombre, profesor –animate: perro, gato –inanimate: libro, pescado, bocadillo, silla –locative: Barcelona, camino

52 Nouns’ semantic categories lex(clara, name, human). lex(maria, name, human). lex(juan, name, human). lex(barcelona, name, locative).

53 Nouns’ semantic categories lex(libro, n, K, libro(K), inanimate). lex(hombre, n, K, hombre(K), human). lex(profesor, n, K, profesor(K), human). lex(perro, n, K, perro(K), animate). lex(gato, n, K, gato(K), animate). lex(camino, n, K, camino(K), locative).

54 Verbs’ semantic categories lex(piensa, v, S, [arg(en,O)], pensar_en(S,O), sem(human, [X])). lex(habla, v, S, [arg(de,O),arg(con,O1)], comunica(S,O,O1), sem(human, [X,human])). lex(está, v, S, [arg(en,O)], locative(S,O), sem(X, [locative])). lex(lee, v, S, [arg(null,O)], leer(S,O), sem(human, [inanimate])).

55 Grammar 5: semantic constraints v(S,A,F,sem)  [Word],{lex(Word,v,S,A,F,sem) }. name(Word,sem)  [Word],{lex(Word,name,sem)}. n(Word,sem)  [Word],{lex(Word,n,sem)}. np(K,S2,F,sem)  det(K,S1,S2,F), n(K,S1,sem). np(K,F,F,sem)  name(K,sem).

56 Grammar 5: semantic constraints compl([ ],S,S,[ ])  [ ]. compl([arg(X,K) | Y],S1,S,[sem | sem2])  p(X), np(K,S2,S,sem), compl(Y,S1,S2,sem2). s(S)  np(K,S2,S,sem1), v(K,X,S1,sem(sem1,list-sem)), compl(X,S1,S2,[list-sem]).

57 Formalismes d’unificació i gramàtiques lògiques Formalismes basats en unificació ⊂ Gramàtiques lògiques Llenguatge habitual d’implementació: Prolog Característiques –Unificació com a mecanisme bàsic de composició entre constituents –Aproximació sintagmàtica com a forma bàsica de descripció gramatical

58 Formalismes d’unificació Història Q-Systems (Colmerauer, 1972) Prolog (Colmerauer, 1973) Gramàtiques de Metamorfosi (Colmerauer, 1975) Gramàtiques de Clàusules Definides (DCGs) (Pereira, Warren, 1980)

59 Notació Afirmacions (fets)  home (X)  Condicions (regles)  mortal (X)  home (X) Negacions (consultes)  immortal(X) Contradicció 

60 Anàlisi gramatical com a demostració de teoremes L'expressió de la gramàtica i el lexicó com clàusules de Horn permet l’aplicació de la resolució i raonament per refutació com a procediment d’anàlisi. (1) oració (X,Y)  gnom(X,Z), gver(Z,Y) (2) gnom(X,Y)  art(X,Z), nom(Z,Y) (3) gver(X,Y)  ver(X,Y) Gramàtica (4) art(X,Y)  el (X,Y) (5) nom(X,Y)  gos(X,Y) (6) ver(X,Y)  borda(X,Y) Lexicó

61 Exemple (1) el gos borda (7) el(1,2)  (8) gos(2,3)  (9) borda (3,4)  TEOREMA a demostrar oració (1,4)  Raonant per refutació hauríem de negar  oració (1,4) i per derivació descendent demostrar una contradicció

62 Exemple (2)  Frase (1,4) (R1) (X  1, Y  4) per unificació  gnom (1,Z), gver(Z,4) (R2) i (R4) aplicades a gnom(1,Z) i art(1,U)  art(1,U),nom(U,Z), gver(Z,4)  el(1,U), nom(U,Z), gver(Z,4) (R7) (U  2)  nom(2,Z), gver(Z,4) (R5) i (R8) (Z  3)  gos(2,3), gver(3,4)  gver(3,4) (R3) i (R6) i (R9)  ver(3,4)  borda(3,4) El gos borda

63 Exemple (3) Frase (1,4)   gnom (1,Z), gver(Z,4)  art(1,U), nom(U,Z), gver(Z,4)  el, nom(2,Z), gver(Z,4)  nom(2,Z), gver(Z,4)  gos(2,Z), gver(Z,4)  gver(3,4)  ver(3,4)  borda(3,4) El gos borda Interpretació directa a Prolog !!

64 Semantic interpretation It consists of constructing a representation of the sentences in some formal system. In general, it’s an intractable problem. It’s simplified supposing that the semantics of a sentence can be constructed from the semantics of its parts: compositional semantics. Some characteristics of the language have to be treated separately: references, omissions, context.

65 Strategies Sequential (syntactic → semantic) Parallel (syntactic + semantic)

66 Sequential interpretation Ambiguity problems There might be more than a syntactic interpretation and all of them have to be considered. Main advantage The semantic analysis starts from a syntactically correct sentence.

67 Parallel interpretation Syntactic rules include semantic information The result obtained is an analysis tree and one or more interpretations. Main problem The syntactic interpretation potentially not confirmed until the end. Main advantage Being able to discard (partially) correct syntactic interpretations which have no associated semantic interpretation.

68 Representation system The semantic representation has to allow: to manage quantification, predication, negation, modality (believes) to resolve lexical (polysemy) and syntactic ambiguity to manage inferences (inheritance, default reasoning) In general, a variety of FOL which is adequate to the application domain is used.

69 Representation system The basic representation element is the lexeme: root of a group of words, which are different forms of “the same word” example: go, gone, going

70 Representation system Examples of representation: Names (or proper nouns) correspond to constants. Intransitive verbs to unary predicates: Juan ríeríe(juan) Transitive verbs to higher arity predicates: Juan lee el Quijote lee(juan, quijote) Nouns to predicates over variables: El hombrehombre(X) Adjectives to unary predicates: La casa grandegrande(X)  casa(X)

71 Representation system The representation usually consist of an analysis tree and a composition function. sem S = f S (sem NP, sem VP ) sem NP = f SN (sem ART, sem N ) sem ART = f ART (sem el) S NP NAME Adrià VP V menja NP ART N bacallà el

72 Lambda cálculo (1) Las funciones de composición son normalmente  expresiones Lexicón (ha de tener en cuenta la polisemia): Juan → np, juan Maria → np, maria ríe → vi,  x. reir(x) ama a → vt,  x.  y. amar(y,x)

73 Lambda cálculo (y 2) Gramática (incluye el orden de aplicación de los parámetros): Frase → GN FV, (2.1) GN → np, (1) FV → vi, (1) FV → vt GN, (1.2)


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