Some Uses of Higher-Order Logic in Computational Linguistics

Some Uses of Higher-Order Logic in Computational Linguistics Dale A. Miller and Gopalan Nadathur Computer and Information Science University of Pennsylvania Philadelphia, PA 19104 - 3897 Abstract Consideration of the question of meaning in the frame- work of linguistics often requires an allusion to sets and other higher-order notions. The traditional approach to representing and reasoning about meaning in a computa- tional setting has been to use knowledge representation sys 7 tems that are either based on first-order logic or that use mechanisms whose formal justifications are to be provided after the fact. In this paper we shall consider the use of a higher-order logic for this task. We first present a ver- sion of definite clauses (positive Horn clauses) that is based on this logic. Predicate and function variables may oc- cur in such clauses and the terms in the language are the typed h-terms. Such term structures have a richness that may be exploited in representing meanings. We also de- scribe a higher-order logic programming language, called ~Prolog, which represents programs as higher-order defi- nite clauses and interprets them using a depth-first inter- preter. A virtue of this language is that it is possible to write programs in it that integrate syntactic and seman- tic analyses into one computational paradigm. This is to be contrasted with the more common practice of using two entirely different computation paradigms, such as DCGs or ATNs for parsing and frames or semantic nets for semantic processing. We illustrate such an integration in this lan- guage by considering a simple example, and we claim that its use makes the task of providing formal justifications for the computations specified much more direct. 1. Introduction The representation of meaning, and the use of such a representation to draw inferences, is an issue of central con- cern in natural language understanding systems. A theoret- ical understanding of meaning is generally based on logic, and it has been recognized that a higher-order logic is par- ticularly well suited to this task. Montague, for example, used such a logic to provide a compositional semantics for simple English sentences. In the computational framework, knowledge representation systems are given the task of rep- resenting the semantical notions that are needed in natural This work has been supported by NSF grants MCS-82- 19196-CER, MCS-82-07294, AI Center grants MCS-83- 05221, US Army Research Office grant ARO-DAA29-84- 9-0027, and DARPA N000-14-85-K-0018. language understanding programs. While the formal justi- fications that are provided for such systems is usually log- ical, the actual formalisms used are often distantly related to logic. Our approach in this paper is to represent mean- ings directly by using logical expressions, and to describe the process of inference by specifying manipulations on such expressions. As it turns out, most programming languages are poorly suited for an approach such as ours. Prolog, for instance, permits the representation and the examina- tion of the structure of first-order terms, but it is not easy to use such terms to represent first-order formulas which …

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