1 / 32

Semantic Composition with l -DRT

Semantic Composition with l -DRT. Christof Rumpf Heinrich-Heine-Universität Düsseldorf http://www.phil-fak.uni-duesseldorf.de/~rumpf/ 30.07.2003. the problem(s). semantic construction

Download Presentation

Semantic Composition with l -DRT

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Semantic Composition with l-DRT Christof Rumpf Heinrich-Heine-Universität Düsseldorf http://www.phil-fak.uni-duesseldorf.de/~rumpf/30.07.2003

  2. the problem(s) • semantic construction • Given a text in a natural language, is there a systematic method for constructing the representation of its meaning from the meaning of its parts (Frege)? • inference • Can we draw inferences with these representations? • computation • Can all this be automated?

  3. the framework • first-order logic (fol) • l-calculus + (context free) grammar • DRT - Dicourse Representation Theory This framework has proved to be useful in the machine translation project Verbmobil : 1993 - 2000, 166 million DM, 375 publications, where the funding came from the BMBF and some industry partners.

  4. the sources • You will find almost all the material from this presentation (and much more else) in: • Blackburn, Patrick & Johan Bos (to appear) Representation and Inference for Natural Language. Stanford: CSLI Publications.and for free at • http://www.comsem.org

  5. levels of semantic representation • word level • lexical semantics: lexicalist l-abstractions of fol expressions that specify the combinatorial potential at the phrase level • representations may be complex • phrase level • semantic composition with functional application • results in very simple phase structure rules • discourse level • l-DRT: l-calculus over discourse representation structures (DRSs) for word, phrase and discourse levels

  6. simplified composition model SPeter likes Marylike(peter, mary) CFG:S  NP VPVP  V NP Is this rule-based?What does the rule looks like? VPlikes Marylike(?, mary) NPPeterpeter The process of variable binding should be guided by explicit rules. Vlikeslike(?, ?) NPMarymary

  7. l-calculus • l-calculus can be used as a metalanguage over fol to serve as a ‚glue language‘ for fol expressions. • The l-operator binds variables over individuals and predicates (2nd order logic) with l-abstraction. • Variables can be associated with arguments via functional application. Access to variables is constrained by the sequence of l-operators. • Substitutions of variables with arguments are performed by an operation called b-conversion.

  8. l-abstraction & functional application • l-abstraction: lx.woman(x) • The l-operator binds the occurrence of x in the one-place predicate woman and marks it as a landing place for an argument. • functional application: lx.woman(x)@mary • The term mary is applied to the l-expression with the operator @, which denotes functional application. The operator has the shape functor@argument. Argument substitution will be done by b-conversion.

  9. b-conversion • Functional applications are instructions to perform b-conversion:ly.lx.likes(x, y)@maryb-conversion yieldslx.likes(x, mary) • b-conversion substitutes the leftmost variable in the sequence of l-abstractions with the rightmost argument that is attached by functional application. This eliminates the l-abstraction for the variable.

  10. a-conversion • The variables of the two terms in functor@argument structures need to be distinct to make b-conversion sound. a-conversion renames bound variables. • without a-conversion: ly.lx.like(x,y)@xlx.like(x, x) • with a-conversion:ly.lx.like(x,y)@xa ly1.lx1.like(x1,y1)@x2ly1.lx1.like(x1,y1)@x2 lx1.like(x1,x2)

  11. quantifiers • every: lP.lQ.x(P@x Q@x) • beetle: ly.beetle(y) • every beetle:lP.lQ.x(P@x  Q@x)@ly.beetle(y) • by b-conversion: 1. lQ.x(ly.beetle(y)@x Q@x) 2. lQ.x(beetle(x)  Q@x) • every beetle hums: lQ.x(beetle(x) Q@x)@ly.hum(y)x(beetle(x) ly.hum(y)@x)x(beetle(x)  hum(y)) • exists: lP.lQ.x(P@x Q@x)

  12. proper names • Quantified noun phrases (in subject position) are functors that take verbs as arguments to build sentences:lQ.x(beetle(x) Q@x)@ly.hum(y) • Proper names are raised to functors to allow for uniform composition:lP.P@mary@ly.hum(y)ly.hum(y)@maryhum(mary)

  13. transitive verbs • Transitive verbs are represented as functors that take their object NP‘s semantic representation as an argument: lQ.lx.(Q@ly.like(x, y))@lP.P@mary lx.(lP.P@mary@ly.like(x, y)) lx.(ly.like(x, y)@mary) lx.like(x, mary)

  14. semantic construction Finally, compared with the earlier example this is rule guided semantic composition: we know in advance, where the arguments have to take place. S (NP@VP)Peter likes Marylike(peter, mary) VP (V@NP)likes Marylz.like(z,mary) NPPeterlP.P@peter VlikeslQ.lx.Q@ly.like(x, y) NPMarylP.P@mary

  15. Prolog DCG s(NP@VP)  np(NP), vp(VP).vp(V@NP)  tv(V), np(NP).vp(VP)  iv(V). Syntaxnp(NP)  pn(PN).np(Det@N)  det(Det), n(N). det(lP.lQ.X(P@X  Q@X))  [every].n(lY.beetle(Y))  [beetle].pn(lP.P@mary)  [mary]. Lexiconiv(lY.hum(Y))  [hums].tv(lQ.lX.Q@lY.like(X, Y))  [likes]. ?- s([every,beetle,likes,mary],[ ],S1), betaconvert(S1,S2).S1 = (lP.lQ.X(P@X  Q@X)@lY.beetle(Y))@ (lQ.lX.Q@lY.like(X, Y)@lP.P@mary)S2 = X(beetle(X)  like(X, mary)) The l-expressions in the lexicon have to be converted to linearized Prolog notation.

  16. DRT • Discourses are sequences of sentences. • In discourse representation theory (DRT) discourses are represented as discourse representation structures (DRSs) which contain discourse referents and conditions on discourse referents (individuals). • DRSs provide a language that restricts expressiveness to possible discourse structures.

  17. x1, ..., xn g1, ..., gm discourse representation structures • If x1, ..., xn (n 0) are discourse referents and g1, ..., gm (m 0) are conditions, then is a DRS. • If R is a relation symbol of arity n and x1, ..., xn are discourse referents, then R(x1, ..., xn) is a condition. • If t1 and t2 are discourse referents or constants, then t1 = t2 is a condition. • If K1 and K2 are DRSs,then K1 K2 and K1K2 are conditions. • If K is a DRS then K is a condition. • Nothing else is a DRS.

  18. x beetle(x)hum(x) indefinite noun phrases DRS for a beetle hums fol: x beetle(x)  hum(x) discourse referent x introduced by the noun phrase

  19. x x=mary  hum(x) proper names, negation DRS for mary does not hum fol: x hum(x)  x=mary discourse referent x introduced by the noun phrase

  20. x beetle(x)  hum(x) universal quantifiers DRS for every beetle hums fol: x beetle(x)  hum(x)

  21. semantics of DRSs • DRSs can be translated to a subset of fol with equality. • One can give DRSs a model theoretic semantics in parallel to the equivalent fol expressions (satisfiability). • DRSs include a notion of accessibility for variables, what introduces deliberate restrictions on possible discourse structures • These restrictions constitute DRT as a theory on discourse structures.

  22. accessibility • accessibility of discourse referents between nested DRSs is restricted • discourse referents of DRS K1 are accessible from DRS K2 iff • K1 subordinates K2 or • K1 = K2

  23. subordination Let K1 and K2 be DRSs. K1 subordinates K2 iff • K1 contains a condition K2 • K1 contains a condition K2 K, where K is some DRS • K1 contains a condition K2 K or K K2 for some DRS K • K1 K2 is a condition in some DRS K • Some DRS K subordinates K2, and K1 subordinates K (transitvity of subordination)

  24. x y beetle(x)fly(x)hum(y)x=y pronoun resolution DRS for a beetle flies. it hums • How can we construct this? • standard construction algorithm • l-DRT (explication follows) fol: x y beetle(x)  fly(x)  hum(y)  x=y

  25. x beetle(x)  hum(y)y=? fly(x) accessibility conflict DRS for every beetle flies. it hums variable x not accessible for pronoun resolution fol: x beetle(x)  hum(x)

  26. l-DRT • In l-DRT we define l-calculus over DRSs. So we have • l-abstraction over DRSs and discourse referents • functional application of DRSs and discourse referents • b- and a-conversion of those functional applications • In addition, we use an operation  (merge) to build a DRS from two DRSs by the • union of the discourse referents • union of the conditions

  27. beetle: lx. a: lP.lQ.  P@x  Q@x hums: lx. beetle(x) hum(x) love(x,y) x x loves: lP.lx.P@ly. every: lP.lQ.  P@x  Q@x some lexical entries

  28. hum(x) xbeetle(x)  every beetle hums: lQ. hum(x) xbeetle(x)  Q@x every beetle: lQ. x beetle(x) beetle: lx.  P@x  Q@x every: lP.lQ. example analysis S (NP@VP) hums: lx. NP (Det@N)

  29. x y beetle(x)fly(x)hum(y)x=y x beetle(x)fly(x) y hum(y)y=? pronouns • Pronouns introduce variables that need special anaphoric bindings. • One has to find an accessibleandappropriate (antecedent) discourse referent. • Appropiateness can be triggered with additional constraints like gender congruence and the type of the pronoun (reflexivity: it vs. itself). • We introduce a special notation a-DRSs, where a stands for anaphoric. • Not functional application, but our merge operation has to be extended to cope with a-DRSs. • Analysis of a beetle flies. it hums: =  y

  30. coreference resolution • Anaphoric binding of pronouns is just one instance of the corefence resolution problem. • There are (many?) other instances of this problem, for example synonyms: Abendstern, Morgenstern; Current President of Germany, Gerhard Schröder, Herr Schröder etc. • Evaluation of the coreference resolution problem in current information technology systems is significantly poor: < 58% f-measure (geometrical middle of precision and recall, which means correctness and completeness)  here there seems to be a lot of work to do.

  31. some extensions of l-DRT • focussing • Anaphoric binding in large texts is not unlimited - what are the appropriate distance limits for bindings in a certain context? • quantifier scope ambiguities • The most recent solutions are based on underspecification, where earlier approaches used storage techniques. • presupposition resolution • What are the pieces of information that can be taken for granted in a context?

  32. conclusion • Semantic composition is interesting not only for philosophers, linguists and other friends of the science of language and/or mind. • It is also a crucial problem for current well funded work on information technology. • How do/can/would we exploit this modern ‚gold rush‘?

More Related