DEFINITE CLAUSE GRAMMARS Ivan Bratko University of Ljubljana Faculty of Computer and Information Sc.

DEFINITE CLAUSE GRAMMARS

Ivan Bratko

University of Ljubljana

Faculty of Computer and Information Sc.

DCG = Definite Clause Grammar

DCG notation in Prolog

Context-free grammars in DCG

Introducing context-dependence through arguments

Prolog goals in grammars rules

Defining semantics with DCG

Natural language syntax in DCG

Defining meaning of natural language

A BNF grammar

<s> ::= a b | a <s> b

Grammar generates / recognises

s

a s b

Generation Recognition

a s b

a b

Sentence = a a a b b b

COMMAND SEQUENCES FOR A ROBOT

up

up up down up down

CORRESPONDING BNF GRAMMAR

<move> ::= <step> | <step> <move>

<step> ::= up | down

CORRESPONDING DCG

move --> step.

move --> step, move.

step --> [up].

step --> [down].

SENTENCES IN DCG

DCG expects a sentence to be represented as difference list

aabb ~ [a,a,b,b], []

~ [a,a,b,b,c], [c]

~ [a,a,b,b,x,y,z], [x,y,z]

~ ...

QUESTIONS TO DCG

?- move( [up,down,up], []).

yes

?- move( [up, X, up], []).

X = up;

X = down;

no

?- move( [ up, down, up, a, b, c], [ a, b, c]).

yes

PROLOG CONVERTS DCG INTO A RECOGNITION PROGRAM

move( List, Rest) :-

step( List, Rest).

move( List1, Rest) :-

step( List1, List2),

move( List2, Rest).

step( [up | Rest], Rest).

step( [down | Rest], Rest).

FROM DCG TO STANDARD PROLOG

DCG rule:

move --> step, move.

Corresponding Prolog rule:



move( List2, Rest).



move( List2, Rest).

move

step move

Rest

List2

List1

FROM DCG TO STANDARD PROLOG

A SIMPLE NATURAL LANGUAGE DCG

The cat scares the mouse.

det noun verb det noun

noun_phrase noun_phrase

verb_phrase

sentence

A SIMPLE NATURAL LANGUAGE DCG

sentence --> noun_phrase, verb_phrase.

verb_phrase --> verb, noun_phrase.

noun_phrase --> determiner, noun.

determiner --> [ the].

noun --> [ cat].

noun --> [ cats].

noun --> [ mouse].

verb --> [ scares].

verb --> [ scare].

THIS GRAMMAR GENERATES

[ the, cat, scares, the, mouse]

[ the, mouse, scares, the, mouse]

[ the, cats, scare, the, mouse]

[ the, cats, scares, the, mouse]

CONTEXT DEPENDENT!

NUMBER AGREEMENT CAN BE FORCED

BY ARGUMENTS sentence( Number) --> noun_phrase( Number), verb_phrase( Number). verb_phrase( Number) --> verb( Number), noun_phrase( Number1).

noun_phrase( Number) --> determiner( Number), noun( Number).

noun( singular) --> [ mouse].noun( plural) --> [ mice].verb( singular) --> [scares].verb( plural) --> [scare].

NUMBER AGREEMENT CAN BE FORCED

BY ARGUMENTS

?- sentence( Number, [the, cats, scares, the, mouse], []).

no

?- sentence( Number, [the, cats, scare, the, mouse], []).

Number = plural

CONSTRUCTING PARSE TREES

[ up, down, up]

move

step move

up step move

down step

up

DCG TO CONSTRUCT PARSE TREES

Tree = move( step(up), move( step(down), ...))

move( move( Step)) --> step( Step).

move( move( Step, Move)) -->

step( Step), move( Move).

step( step( up)) --> [up].

step( step( down)) --> [down].

DEFINING MEANING

Define: Meaning of move = Distance travelled

meaning ( ‘up up down up’) = 1+1-1+1 = 2

meaning( ‘up up down up’) =

meaning( ‘up’) + meaning( ‘up down up’)

FROM PARSE TREE TO MEANING

To find meaning of sentence:

(1) Construct parse tree

(2) Process parse tree

MEANING OF MOVES TREE

meaning( move( Step, Move), Dist) :-

meaning( Step, D1),

meaning( Move, D2),

Dist is D1 + D2.

meaning( step( up), 1).

meaning( step( down), -1).

INTERLEAVING SYNTAX AND MEANING

sentence parse tree meaning

Avoid parse tree, encode meaning directly in DCG

PROLOG goals in DCG: {Goal}

move( Dist) --> step( Dist).

move( Dist) --> step( D1), move( D2), {Dist is D1 + D2}.

step( 1) --> [ up]. step( -1) --> [ down]. ?- move( D, [ up, up, down, up], [ ] ). D = 2

MEANING OF NATURAL LANGUAGE

Representation of meaning = ?

Depends on use of meaning,

e.g. natural language querying

Logic is a good candidate for representing meaning

SOME MEANINGS IN LOGIC

Sentence Formalised meaning

``John paints’’ paints( john)

``John likes Annie’’ likes( john, annie)

SOME MEANINGS IN LOGIC

Sentence

``A man paints’’

Formalised meaning

exists( X, man(X) and paints(X))

Note: ``paints’’ is intransitive verb, ``likes’’ is trans. verb

A SYNTAX

sentence ---> noun_phrase, verb_phrase.

noun_phrase --> proper_noun.

verb_phrase --> intrans_verb.

verb_phrase --> trans_verb, noun_phrase.

intrans_verb --> [ paints].

trans_verb --> [ likes].

proper_noun --> [ john].

...

INCORPORATING MEANING

% “john’’ means “john’’

proper_noun( john) --> [ john].

% “paints’’ means “paints( X)’’

intrans_verb( paints( X)) --> [ paints].

COMBINING MEANING OF NOUN PHRASE AND VERB PHRASE

“John paints”

sentence

noun_phrase verb_phrase

proper_noun intrans_verb john paints


paints( john)

sentence

john noun_phrase verb_phrase paints( X)

john proper_noun intrans_verb paints( X) john paints


john + paints( X) = paints( john)

Meaning of NP Meaning of sentence

Meaning of VP

COMBINING OF MEANING OF VERB PHRASE AND NOUN PHRASE

noun_phrase( NP) --> proper_noun( NP).

verb_phrase( VP) --> intrans_verb( VP).

sentence( S) ---> noun_phrase( NP), verb_phrase( VP), { compose( NP, VP, S) } .

COMPOSING NP AND VP MEANINGS

actor( paints( X), X).

compose( NP, VP, VP) :- % Meaning of sentence is VP

actor( VP, NP). % Where actor in VP is NP

?- compose( john, paints( X), S).

S = paints( john)

MORE ELEGANT

DEFINE MEANING OF TRANSITIVE VERB

SO THAT ACTOR BECOMES EXTRA ARGUMENT

intrans_verb( Actor, paints( Actor)) --> [ paints].

verb_phrase( Actor, VP) --> intrans_verb( Actor, VP).

sentence( VP) ---> noun_phrase( Actor), verb_phrase( Actor, VP).

This makes “slots” in meaning “visible”

paints( Actor)

Slot to be filled by context

MEANING OF TRANSITIVE VERBS

“likes” means likes( Somebody, Something)

trans_verb( Somebody, Something, likes(Somebody,Something)) -->

[ likes].

verb_phrase( Somebody, VP) -->

trans_verb( Somebody, Something, VP),

noun_phrase( Something).

MEANING OF DETERMINERS “A” AND “EVERY”

“A man paints” means:

exists( X, man( X) and paints( X) )

Determiner “a” dictates the meaning of whole sentence!

“a man” means:

exists( X, man( X) and Assertion)

Statement about X

MEANING OF “A”

“a” means:

There is some X such that:

X has some property and

some assertion holds about X.

exists( X, Property and Assertion)

Make X, Property and Assertion visible:

determiner( X, Property, Assn, exists( X, Property and Assn)) -->

[ a].

INTEGRATING MEANING OF DETERMINERS AND OTHER PHRASES

sentence

noun_phrase verb_phrase

determiner noun intrans_verb

a man paints

paints(X)man(X)exists( X, P and A)

exists( X, man(X) and A) paints(X)

exists( X, man(X) and paints(X) )


sentence( S) -->

noun_phrase( X, Assn, S), verb_phrase( X, Assn).

noun_phrase( X, Assn, S) -->

determiner( X, Prop, Assn, S), noun( X, Prop).

noun_phrase( X, Assn, Assn) -->

proper_noun( X).


verb_phrase( X, Assn) -->

intrans_verb( X, Assn).

determiner( X, Prop, Assn, exists( X, Prop and Assn)) --> [a].

noun( X, man( X)) --> [ man].

intrans_verb( X, paints(X)) --> [paints].

DETERMINER “EVERY”

“Every woman dances” means:

all( X, woman( X) ==> dances( X) )

determiner( X, Prop, Assn, all( X, Prop ==> Assn ) )

--> [ every].

RELATIVE CLAUSES

“Every man that paints admires Monet”

SYNTAX:

noun_phrase --> determiner, noun, rel_clause.

rel_clause --> [ that], verb_phrase.

rel_clause --> [ ]. % Empty relative clause

RELATIVE CLAUSES


MEANING:

all( X, man( X) and paints( X) ==> admires( X, monet) )

RELATIVE CLAUSES

MEANING, GENERAL FORM

all( X, Prop1 and Prop2 ==> Assertion )

noun verb phrase verb phrase

of rel. clause of sentence

RELATIVE CLAUSES: SYNTAX AND MEANING

rel_clause( X, Prop1, Prop1 and Prop2) -->

[ that ], verb_phrase( Prop2).

noun_phrase( X, Assn, S) -->

determiner( X, Prop12, Assn, S), noun( X, Prop1),

rel_clause( X, Prop1, Prop12).

rel_clause( X, Prop1, Prop1) --> [ ].

COMPLETE GRAMMAR

% Meaning of subset of natural language

:- op( 100, xfy, and).

:- op( 150, xfy, =>).

sentence( S) -->

noun_phrase( X, P, S), verb_phrase( X, P).

noun_phrase( X, P, S) -->

determiner( X, P12, P, S), noun( X, P1), rel_clause( X, P1, P12).

noun_phrase( X, P, P) -->

proper_noun( X).

verb_phrase( X, P) -->

trans_verb( X, Y, P1), noun_phrase( Y, P1, P).

verb_phrase( X, P) -->

intrans_verb( X, P).

COMPLETE GRAMMAR, CTD.

rel_clause( X, P1, P1 and P2) -->

[that], verb_phrase( X, P2).

rel_clause( X, P1, P1) --> [].

determiner( X, P1, P, all( X, P1 => P)) --> [every].

determiner( X, P1, P, exists( X, P1 and P)) --> [a].

noun( X, man(X)) --> [man].

noun( X, woman(X)) --> [woman].

proper_noun( john) --> [john].

proper_noun( annie) --> [annie].

proper_noun( monet) --> [monet].

trans_verb( X, Y, likes( X, Y)) --> [ likes].

trans_verb( X, Y, admires( X, Y)) --> [admires].

intrans_verb( X, paints(X)) --> [paints].

SOME TEST SENTENCES

% Some tests

test1( M) :-

sentence( M, [john,paints],[]).

test2( M) :-

sentence( M, [a, man, paints], []).

test3( M) :-

sentence( M, [every,man,that,paints,admires,monet],[]).

test4( M) :-

sentence( M, [annie,admires,every,man,that,paints],[]).

test5( M) :-

sentence( M, [every,woman,that,admires,a,man,that,paints,likes,monet],[]).

EXAMPLES OF SENTENCES THIS GRAMMAR HANDLES


“Annie admires every man that paints”

“Every woman that admires a man that paints likes Monet”

Meaning constructed for this sentence:

all( X, woman( X) and exists( Y, ( man( Y) and paints (Y))

and admires( X, Y) ) ==> likes( X, monet ) )

USE IN QUESTION ANSWERING

Meanings in logic can be translated into Prolog:

admires( X, monet) :-

man( X), paints( X).

admires( annie, X) :-

man( X), paints( X).

likes( X, monet) :-

woman( X), man( Y), paints( Y), admires( X, Y).

“Does Annie admire anybody who admires Monet?”

?- admires( annie, X), admires( X, monet).

GENERATING SENTENCES

Our grammar also generates sentences with given meaning

?- sentence( likes(john,annie), S, []).

S = [john,likes,annie]

?- sentence( exists(X, man(X) and paints(X)), S, []).

S = [a,man,paints]

LANGUAGE TRANSLATION WITH DCG

Translate from language 1 to langauage 2:

?- ...,

sentence_lang1( Meaning, Sent1, []),

sentence_lang2( Meaning, Sent2, []).

Can also be used for program compilation

(Spakowicz, BYTE, Aug. 1987)

?- ...,

program_source( M, SourceProg, []), % Parse

program_target( M, TargetProg, []). % Generate

DEFINITE CLAUSE GRAMMARS Ivan Bratko University of Ljubljana Faculty of Computer and Information Sc.

Documents

Transcript of DEFINITE CLAUSE GRAMMARS Ivan Bratko University of Ljubljana Faculty of Computer and Information Sc.