Computational Semantics of Mass Terms

COMPUTATIONAL SEMANTICS OF MASS TERMS Jan Tore l..¢nning Department of Mathematics University of Oslo P.O. Box 1053, Blindern 0316 Oslo 3, Norway ABSTRACT Although the formalisms normally used for describ- ing the semantics of natural languages are far from computationally tractable, it is possible to isolate particular semantic phenomena and interpret them within simpler formal systems. Quantified mass noun phrases is one such part. We describe a simple formal system suitable for the interpretation of quantified mass noun phrases. The main issue of this paper is to develop an algorithm for deciding the validity of sentences in the formal system and hence for deciding the validity of natural language infer- ences where all the involved noun phrases are quantified mass noun phrases. The decision proce- dure is based on a tableau calculus. INTRODUCTION A formal semantics for a part of a natural language attempts to describe the truth conditions for sen- tences, or propositions expressed by sentences, in model theoretic terms, and thereby also the relation of valid inferences between sentences. From the point of view of computational linguistics and natu- ral language understanding, it is important whether this relation of entailment can be made computa- tional. In general, the question must be answered in the negative. All proposed formal semantics of, say, English are at least as complex as first order logic and hence at best semi-decidable, which means that if a sentence 13 is a logical consequence of a set of sen- tences Y., then there exists a proof for [3 from ~, but no effective way to find such a proof. Several pro- posals use even more complex logics, like the higher order intensional logic used in Montague grammar, which has no deductive theory at all. We will not oppose to the view that English in- corporates at least the power of first order logic and that even more complex formalisms may be needed to represent the meaning of all aspects of English. But we believe there are two different possible strategies when one is to study one particular se- mantic phenomenon in natural languages. The first one is to try to interpret the particular phenomenon into a system that attempts to capture all semantic aspects of the natural language. The other slrategy is to try to isolate the particular semantic phe- nomenon one wants to study and to build a semantic interpretation suited for this particular phenomenon. By following the latter strategy it might be possible to find systems simpler than even first order logic that reflect interesting semantic phenomena, and in particular to come up with systems that are compu- tationally tractable. Quantified mass noun phrases is one such phe- nomenon that can be easily isolated. The properties particular for the semantics of quantified mass terms have been difficult to capture in extensions of sys- tems already developed for count terms, like first or- der logic. However, if one isolate the mass terms and tries to interpret only them, it is possible to build a …

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