An Algebra for Semantic Construction in Constraint-based Grammars

An Algebra for Semantic Construction in Constraint-based Grammars Ann Copestake Computer Laboratory University of Cambridge New Museums Site Pembroke St, Cambridge, UK aac@cl.cam.ac.uk Alex Lascarides Division of Informatics University of Edinburgh 2 Buccleuch Place Edinburgh, Scotland, UK alex@cogsci.ed.ac.uk Dan Flickinger CSLI, Stanford University and YY Software Ventura Hall, 220 Panama St Stanford, CA 94305, USA danf@csli.stanford.edu Abstract We develop a framework for formaliz- ing semantic construction within gram- mars expressed in typed feature struc- ture logics, including HPSG. The ap- proach provides an alternative to the lambda calculus; it maintains much of the desirable flexibility of unification- based approaches to composition, while constraining the allowable operations in order to capture basic generalizations and improve maintainability. 1 Introduction Some constraint-based grammar formalisms in- corporate both syntactic and semantic representa- tions within the same structure. For instance, Fig- ure 1 shows representations of typed feature struc- tures (TFSs) for Kim, sleeps and the phrase Kim sleeps, in an HPSG-like representation, loosely based on Sag and Wasow (1999). The semantic representation expressed is intended to be equiv- alent to r name(x, Kim) ∧ sleep(e, x).1 Note: 1. Variable equivalence is represented by coin- dexation within a TFS. 2. The coindexation in Kim sleeps is achieved as an effect of instantiating the SUBJ slot in the sign for sleeps. 3. Structures representing individual predicate applications (henceforth, elementary predi- cations, or EPs) are accumulated by an ap- pend operation. Conjunction of EPs is im- plicit. 1The variables are free, we will discuss scopal relation- ships and quantifiers below. 4. All signs have an index functioning some- what like a λ-variable. A similar approach has been used in a large number of implemented grammars (see Shieber (1986) for a fairly early example). It is in many ways easier to work with than λ-calculus based approaches (which we discuss further below) and has the great advantage of allowing generaliza- tions about the syntax-semantics interface to be easily expressed. But there are problems. The operations are only specified in terms of the TFS logic: the interpretation relies on an intuitive cor- respondence with a conventional logical represen- tation, but this is not spelled out. Furthermore the operations on the semantics are not tightly specified or constrained. For instance, although HPSG has the Semantics Principle (Pollard and Sag, 1994) this does not stop the composition pro- cess accessing arbitrary pieces of structure, so it is often not easy to conceptually disentangle the syntax and semantics in an HPSG. Nothing guar- antees that the grammar is monotonic, by which we mean that in each rule application the seman- tic content of each daughter subsumes some por- tion of the semantic content of the mother (i.e., no semantic information is dropped during com- position): this makes it impossible to guarantee that certain generation algorithms will work ef- fectively. Finally, from a theoretical perspective, it seems clear that substantive generalizations are being missed. Minimal Recursion Semantics (MRS: Copes- take et al (1999), see also Egg (1998)) tight- ens up the specification of …

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