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An environment for specifying properties of dyadic relations and reasoning about them. I: Language extension mechanisms. (English) Zbl 1175.68433
de Swart, Harrie (ed.) et al., Theory and applications of relational structures as knowledge instruments. COST Action 274, TARSKI. Revised papers. Berlin: Springer (ISBN 3-540-20780-5/pbk). Lect. Notes Comput. Sci. 2929, 87-106 (2003).
Summary: 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.
For the entire collection see [Zbl 1029.00017].

68T27 Logic in artificial intelligence
03G15 Cylindric and polyadic algebras; relation algebras
68N17 Logic programming
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