Some Uses of Higher-Order Logic in Computational Linguistics

Consideration of the question of meaning in the framework of linguistics often requires an allusion to sets and other higher-order notions. The traditional approach to representing and reasoning about meaning in a computational setting has been to use knowledge representation systems 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 version of definite clauses (positive Horn clauses) that is based on this logic. Predicate and function variables may occur in such clauses and the terms in the language are the typed λ-terms. Such term structures have a richness that may be exploited in representing meanings. We also describe a higher-order logic programming language, called λProlog, which represents programs as higher-order definite clauses and interprets them using a depth-first interpreter. A virtue of this language is that it is possible to write programs in it that integrate syntactic and semantic 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 language 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. This work has been supported by NSF grants MCS-8219196-CER, MCS-82-07294, AI Center grants MCS-8305221, US Army Research Office grant ARO-DAA2984-9-0027, and DARPA N000-14-85-K-0018.