Download ppt - 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