Higher-Order Coloured Unification and Natural Language Semantics

Higher-Order Coloured Unification and Natural Language Semantics Claire Gardent Computational Linguistics Universit£t des Saarlandes D-Saarbriicken claire@coil, uni-sb, de Michael Kohlhase Computer Science Universit~t des Saarlandes D-Saarbriicken kohlhase¢cs, uni-sb, de Abstract In this paper, we show that Higher-Order Coloured Unification - a form of unification developed for automated theorem proving - provides a general theory for modeling the interface between the interpretation process and other sources of linguistic, non semantic information. In particular, it pro- vides the general theory for the Primary Occurrence Restriction which (Dalrymple et al., 1991)'s analysis called for. 1 Introduction It is well known that Higher-Order Unification (HOU) can be used to construct the semantics of Natural Language: (Dalrymple et al., 1991) - hence- forth, DSP - show that it allows a treatment of VP- Ellipsis which successfully captures the interaction of VPE with quantification and nominal anaphora; (Pulman, 1995; Gardent and Kohlhase, 1996) use HOU to model the interpretation of focus and its interaction with focus sensitive operators, adverbial quantifiers and second occurrence expressions; (Gar- dent et al., 1996) shows that HOU yields a sim- ple but precise treatment of corrections; Finally, (Pinkal, 1995) uses linear HOU to reconstruct under- specified semantic representations. However, it is also well known that the HOU approach to NL semantics systematically over- generates and that some general theory of the in- terface between the interpretation process and other sources of linguistic information is needed in order to avoid this. In their treatment of VP-ellipsis, DSP introduce an informal restriction to avoid over-generation: the Primary Occurrence Restriction (POR). Although this restriction is intuitive and linguistically well- motivated, it does not provide a general theoretical framework for extra-semantic constraints. In this paper, we argue that Higher-Order Coloured Unification (HOCU, (cf. sections 3,6), a restricted form of HOU developed independently for theorem proving, provides the needed general frame- work. We start out by showing that the HOCU approach allows for a precise and intuitive model- ing of DSP's Primary Occurrence Restriction (cf. section 3.1). We then show that the POR can be extended to capture linguistic restrictions on other phenomena (focus, second occurrence expressions and adverbial quantification) provided that the no- tion of primary occurrence is suitably adjusted (cf. section 4). Obviously a treatment of the interplay of these phenomena and their related notion of primary occurrence is only feasible given a precise and well- understood theoretical framework. We illustrate this by an example in section 4.4. Finally, we illustrate the generality of the HOCU framework by using it to encode a completely different constraint, namely Kratzer's binding principle (cf. section 5). 2 Higher-Order Unification and NL semantics The basic idea underlying the use of HOU for NL semantics is very simple: the typed A-calculus is used as a semantic representation language while se- mantically under-specified elements (e.g. anaphors and ellipses) are represented by free variables whose value is determined by solving higher-order equa- tions. For instance, the discourse (la) has (lb) as a semantic representation where the value of R is given …

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