Geometry of Lexico-Syntactic Interaction

Proceedings of EACL '99 Geometry of Lexico-Syntactic Interaction Glyn Morrill Departament de Llenguatges i Sistemes Informhtics Universitat Polit~cnica de Catalunya Jordi Girona Salgado, 1-3 E-08034, Barcelona morrill @lsi.upc.es Abstract Interaction of lexical and derivational semantics---for example substitution and lambda conversion--- is typically a part of the on-line interpretation process. Proof-nets are to categorial grammar what phrase markers are to phrase structure grammar: unique graphical structures underlying equivalence classes of sequential syntactic derivations; but the role of proof-nets is deeper since they integrate also semantics. In this paper we show how interaction of lexical and derivational semantics at the lexico-syntactic interface can be precomputed as a process of off-line lexical compilation comprising Cut elimination in partial proof-nets. Introduction Consider the paraphrase: following examples of (1) a. b. C. Frodo lives in Bag End. Frodo inhabits Bag End. ((in b) (live])) (2) a. b. C. John tries to find Mary. John seeks Mary. ((try (find rn ) ) j) Typically, for at least (lb) and (2b) the normalised semantic forms result from a process of substitution and lambda conversion subsequent to or simultaneous with syntactic derivation. We show how such interaction of lexical and derivational semantics at the lexico- syntactic interface can be precomputed as a process of off-line lexical compilation comprising Cut elimination in partial proof-nets. For accessibility, we devote in the initial sections a considerable proportion of space to an introduction to categorial grammar oriented towards proof-nets; see also Morrill (1994), Moortgat (1996) and Carpenter (1997). 1 Categorial grammar We consider categorial grammar with category formulas F (categories) defined by the following grammar: (3) a. b. F::=A IFV rlF/FIF-F ..4 ::= S I N I CN I PP I ... The categories in A are referred to as atomic and correspond to the kinds of expressions which are considered to be "complete". Fairly uncontroversially, this class may be taken to include at least sentences S and names N; what the class is exactly is not fixed by the formalism. Left division categories A~B ('A under B') are those of expressions (functors) which concatenate with (arguments) in A on the left to yield Bs. Right division categories B/A ('B over A') are those of expressions (functors) which concatenate with (arguments) in A on the right yielding Bs. Product categories A.B are those of expressions which are the result of concatenating an A with a B; products do not play a dominant role here. More precisely, let L be the set of strings (including the empty string e) over a finite vocabulary V and let + be the operation of concatenation (i.e. (L, +, ~) is the free monoid generated by V) 1 . Each category formula A is interpreted as a subset [[A]] of L. When the interpretation of atomic categories has been fixed, that of complex categories is defined by (4). (4) [[AkB]] = {sl Vs'~ [[A]], s'+s~ [[B]] } [[B/A]] = {sl Vs'~ [[A]], s+s'~ [[B]] } [[A.B]] = {Sl+S21Sle [[,4]] & s2~ [[B]] } 1 In fact Lambek …

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