A Lexical Extension of Montague Semantics

Montague\u27s linguistic theory provides a completely formalized account of language in general and natural language in particular. It would appear to be especially applicable to the problem of natural language understanding by computer systems. However the theory does not deal with meaning at the lexical level. As a result, deduction in a system based on Montague semantics is severely restricted. This paper considers lexical extension of Montague semantics as a way to remove this restriction. Representation of lexical semantics by a logic program or semantic net is complex. An alternative representation, called a semantic space, is described. This alternative lacks the expressiveness of a logic program but it offers conceptual simplicity and intrinsically parallel structure

A Theory of Lexical Semantics

The linguistic theory of Richard Montague (variously referred to as Montague Grammar or Montague Semantics) provides a comprehensive formalized account of natural language semantics. It appears to be particularly applicable to the problem of natural language understanding by computer systems. However the theory does not deal with meaning at the lexical level. With few exceptions, lexical items are treated simply as unanalyzed basic expressions. As a result, comparison of distinct lexical meanings or of semantic expressions containing these lexical meanings falls outside the theory. In this paper, I attempt to provide a compatible compatible theory of lexical semantics which may serve as an extension of Montague Semantics

Resolution without Unification

Resolution as an inference procedure forms the basis of most automated theorem-proving and reasoning systems. The most costly constituent of the resolution procedure in its conventional form is unification. This paper describes PCS, a first-order language in which resolution-based inference can be conducted without unification. PCS resembles the language of elementary logic with the difference that singular predicates supplant individual constants and functions. The result is a uniformity in the treatment of individual constants, functions and predicates. An especially costly part of unification is the occur check. Since unification is unnecessary for resolution in PCS, the occur check is completely circumvented. The conditions that would invoke an occur check are properly represented however. In this sense, resolution in PCS can be viewed as a refinement of conventional resolution. PCS does not have an identity relation. Nonetheless, identity can be expressed in PCS and deduction with identical can be performed

Surface Reasoning

Surface reasoning is defined to be deduction conducted in the surface language in terms of certain primitive logical relations. The surface language is a spoken or written natural language (in this paper, English), in contrast to a base language or “deep structure sometimes hypothesized to explain natural language phenomena. The primitive logical relations are inclusion, exclusion and overlap between classes of entities. A calculus for surface reasoning is presented. Then a model for reasoning in this calculus is developed. The model is similar to but more general than syllogistic. In this model, reasoning is represented as construction of fragments (subposets) of lattices. Elements of the lattices are expressions denoting classes of individuals. Strategies to streamline the reasoning process are described. Criteria for strategy selection are proposed

Inexpressiveness of First-Order Fragments

It is well-known that first-order logic is semi-decidable. Therefore, first-order logic is less than ideal for computational purposes (computer science, knowledge engineering). Certain fragments of first-order logic are of interest because they are decidable. But decidability is gained at the cost of expressiveness. The objective of this paper is to investigate inexpressiveness of fragments that have received much attention

A Variable-Free Logic for Mass Terms

This paper presents a logic appropriate for mass terms, that is, a logic that does not presuppose interpretation in discrete models. Models may range from atomistic to atomless. This logic is a generalization of the author\u27s work on natural language reasoning. The following claims are made for this logic. First, absence of variables makes it simpler than more conventional formalizations based on predicate logic. Second, capability to deal effectively with discrete terms, and in particular with singular terms, can be added to the logic, making it possible to reason about discrete entities and mass entities in a uniform manner. Third, this logic is similar to surface English, in that the formal language and English are well-translatable, making it particularly suitable for natural language applications. Fourth, deduction performed in this logic is similar to syllogistic, and therefore captures an essential characteristic of human reasoning