An Environment for Specifying Properties of Dyadic Relations and Reasoning about Them: I: Language Extension Mechanisms

We show how to enhance a low-level logical language, such as the ‘Schröder-Tarski’ calculus of dyadic relations, so as to make it amenable to a friendly usage. An equational formalism of that kind can play a fundamental role in a two-level architecture of logic-based systems. Three forms of definitional extensions are supported: (1) introduction of new term constructors; (2) ‘disguisement’ of special equations under new sentence constructors; (3) templates for parametric lists of sentences that will be actualized in the formation of axiomatic theories. The power of these extension mechanisms, fully supported by a Prolog program, is illustrated through examples and case studies.