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JOURNALS // Fundamentalnaya i Prikladnaya Matematika // Archive

Fundam. Prikl. Mat., 1999 Volume 5, Issue 4, Pages 1191–1197 (Mi fpm439)

On logical description of geometric figures

A. A. Shakirov

M. V. Lomonosov Moscow State University

Abstract: This paper deals with the problem of equivalence of predicate logic formulas, used for description of geometric objects, constructed from a given set of basic figures by set-theoretic operations $\cap,\cup,\overline{\phantom{a}}$. A finite complete system of identities is obtained for a finite basis in the class of the above formulas with finite number of variables.

UDC: 519.717

Received: 01.02.1996



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