Flexible Semantic Composition with DUDES

Transcription

1 Fleible Semantic Composition ith DUDES Philipp Cimiano Web Information Systems Group TU Delft 1 DUDES In this paper e present a novel formalism for semantic construction called DUDES (Dependency-based Underified Discourse REpresentation Structures). The DUDES formalism has been designed to overcome the rigidity of semantic composition based on the lambda calculus (here the order of application is typically fied) and provides some fleibility ith ret to the direction of the dependence and ith ret to the order of application of arguments. In this short paper e present the DUDES formalism and ork through a simple eample. DUDES bears some resemblance to the ork on λ-drt [2] and LUDs [1] as ell as ith the ork of Copestake et al. [4] and represents a generalization of the formalism introduced in [3]. A detailed discussion of the relation to these formalisms is clearly out of the scope of this paper. DUDES are characterized by three main facts. First they represent semantic dependencies and are thus inherently suitable for a dependency-based grammar formalism assuming that syntactic dependencies correspond to semantic dependencies (though the correspondence might be inverted ). Second they eplicitly encode scope relations and are thus able to yield underified representations as output (in contrast to the linear logic approach for LFG [5] here different scopings correspond to different derivations). Third there is one single operation for semantic composition hich is to some etent order-independent (in contrast to traditional lambda-based formalisms) as ell as fleible ith ret to the direction of the syntactic dependency. As the name suggests DUDES builds on DRT [6] and in particular on UDRT [7] in the sense that it relies on labeled DRSs and dominance relations beteen these to talk about scope. First of all e no first formally introduce DUDES: Definition 1 (DUDES) A DUDES is a 7-tuple (m l t U A S C) consisting of 272 Proceedings of the 8th International Conference on Computational Semantics pages Tilburg January c 2009 International Conference on Computational Semantics

2 - A main discourse referent m and a distinguished label l - The type t of the semantic structure (after inserting all arguments) - A set U of UDRS components. These UDRS components are in essence labeled DRSs [6]. - A set of argument quadruples (l v rel type) consisting of i) a label l (the main label of a DUDE inserted as argument ii) the main variable v of the argument DUDE iii) a grammatical relation and iv) a semantic type. - A set S of scope relations beteen labels introduced in U. - A set C of constraints on the arguments e.g. including ontological constraints or selectional restrictions etc. We no give the semantic representation of the entries for our running eample: John likes every nice oman. : every: John: l e t t John() (l e t ) nice: like: e:like(y) (l 1 sub e t t ) (l 2 y ob e t t ) scope(l 1 ) l 1 scope(l 2 ) l 2 l e t nice() (l e t ) oman: Further e introduce the semantic composition operation for DUDES along a dependency tree distinguishing tree cases: Definition 2 (Semantic Composition for DUDES) Let (γ 1 γ 2) be an edge in some DAG (dependency tree LTAG derivation tree or F- Structure DAG). Assume the edge is labeled ith r (a grammatical function) and the semantics of the vertices γ 1 and γ 2 are given by DUDEs as follos: σ 1 := (m 1 l 1 t 1 U 1 A 1 S 1 C 1) and σ 2 = (m 2 l 2 t 2 U 2 A 2 S 2 C 2). Then the result of applying σ 2 to σ 1 is the DUDE σ = σ 1(σ 2) = (m l t U A S C ) here e need to distinguish the folloing cases: if (l v r t 2) A 1 if (l v r t 1) A 2(t 1 = t 2) if (l v r t 1) A 2(t 1 t 2) (Complementation) (Modification) (Inversion) m := m 1 m := m 1 m := m 2 t := t 1 t := t 1 t := t 2 U := U 1 U 2 U := U 1 U 2 U := U 1 U 2 A := A 1\{(l v r t 2)} A := A 1 A := A 2\{(l v r t 1)} S := S 1 S 2 S := S 1 S 2 S := S 1 S 2 C := C 1 C 2 C := C 1 C 2 C := C 1 C 2 v m 2 l l 2 v m 1( m 2) l l 1 v m 1 l l 1 here is the operation of unification beteen variables. Concerning the order of application from the definition of the semantic composition operator it follos that complements and ifiers can be applied in any order but inversions have to be carried out at the end as 273

3 they change the mother DUDES and ould thus inhibit the application of the complements and the ifiers. In the folloing section e sho ho the semantic composition operation defined above applies to a concrete eample. We ill also discuss that our operations still ork if (some of) the dependencies are inverted. 2 A Worked Eample We ill consider the to folloing (possible) analyses for the sentence: John likes every nice oman. corresponding to the NP analysis (a) and DP analysis (b) retively. 2.1 Complementation a) like ohn sub Given the dependency analysis in a) to the right as a result of applying our semantic composition operator for the complementation case e get a DUDES here the argument has been correctly inserted the DRS components and the scope conditions have been merged and one argument has been removed. Note that this as possible because i) the edge as labeled ith the appropriate grammatical relation sub and ii) the types of σ 2 and of the argument match (both are of type e t t ). The resulting DUDES for [[John likes] is shon in b) to the right. (In case of DRS conditions hich are not comple e assume that the functions res and scope are resolved to the identity function.) ob oman every 2.2 Specification and Modification a) b) nice b) like ohn sub ob every oman nice e:like(y) (l 1 sub e t t ) (l 2 y ob e t t ) scope(l 1 ) scope(l 2 ) sub l e t t John() e:like(y) John() (l 2 y ob e t t ) l 1 scope(l 2 ) The to possible dependency analyses for determiner/noun constructions give rise to to configurations corresponding to a) and b) belo for the semantic composition operator. In both cases independent of the fact hether 274

4 the determiner is the dependent or the head e get that first the semantic representation of the adective is applied to the one of the noun (as the ifier has to be applied before the inversion is carried out in configuration a) thus yielding the to configurations in c) and d). a) (l e t ) l e t nice() (l e t ) b) (l e t ) l e t c) l : l l d) (l e t ) nice() (l e t ) (l e t ) l : l l In case c) e have a case of inversion hile in case d) e have a case of complementation. Overall in both cases e yield the folloing DUDES: [every nice oman]= l e t t l l l l 1 l : 2.3 Result After a further semantic composition step (case complementation) applying [every nice oman] (from Sec. 2.2) to [John likes] (from Sec. 2.1) e yield as resulting UDRS: 275

5 e e:like() John() John() l 3 : l : l : l 1 l 3 l l l 2 l l e:like() References [1] J. Bos B. Gambäck C. Lieske Y. Mori M. Pinkal and K. Worm. Compositional semantics in verbmobil. In Proceedings of COLING [2] Johan Bos Elsbeth Mastenbroek Scott Mcglashan Sebastian Millies and Manfred Pinkal. A compositional drs-based formalism for nlp applications. In Proceedings of the International Workshop on Computational Semantics [3] P. Cimiano A. Frank and U. Reyle. UDRT-based semantics construction for LTAG and hat it tells us about the role of adunction in LTAG. In Proceedings of the 7th International Workshop on Computational Semantics pages [4] Ann Copestake Ale Lascarides and Dan Flickinger. An algebra for semantic construction in constraint-based grammars. In Proceedings of ACL [5] Mary Dalrymple John Lamping Fernando C. N. Pereira and Viay Sarasat. Linear logic for meaning assembly. revised version of the (overvie) paper in Proc. of the Workshop on Computational Logic for Natural Language Processing Edinburgh UK [6] H. Kamp and U. Reyle. From Discourse to Logic. Kluer [7] Ue Reyle. Dealing ith ambiguities by underification: Construction representation and deduction. Journal of Semantics 10(2):