Taxonomic Syntax for First-Order Inference

Most knowledge representation languages are based on classes and taxonomic relationships between classes. Taxonomic hierarchies without defaults or exceptions are semantically equivalent to a collection of formulas in first order predicate calculus. Although designers of knowledge representation languages often express an intuitive feeling that there must be some advantage to representing facts as taxonomic relationships rather than first order formulas, there are few, if any, technical results supporting this intuition. We attempt to remedy this situation by presenting a taxonomic syntax for first order predicate calculus and a series of theorems that support the claim that taxonomic syntax is superior to classical syntax.

Natural Language Syntax and First Order Preference

We have argued elsewhere that first order inference can be made more efficient by using non-standard syntax for first order logic. In this paper we show how a fragment of English syntax under Montague semantics provides the foundation of a new inference procedure. This procedure seems more effective than corresponding procedures based on either classical syntax of our previously proposed taxonomic syntax. This observation may provide a functional explanation for some of the syntactic structure of English.

Syntax-Based Analytic Reading of Musical Scores

As part of a larger research project in musical structure, a program has been written which "reads" scores encoded in an input language isomorphic to music notation. The program is believed to be the first of its kind. From a small number of parsing rules the program derives complex configurations, each of which is associated with a set of reference points in a numerical representation of a time-continuum. The logical structure of the program is such that all and only the defined classes of events are represented in the output. Because the basis of the program is syntactic (in the sense that parsing operations are performed on formal structures in the input string), many extensions and refinements can be made without excessive difficulty. The program can be applied to any music which can be represented in the input language. At present, however, it constitutes the first stage in the development of a set of analytic tools for the study of so-called atonal music, the revolutionary and little understood music which has exerted a decisive influence upon contemporary practice of the art. The program and the approach to automatic data-structuring may be of interest to linguists and scholars in other fields concerned with basic studies of complex structures produced by human beings.