Involutive Brouwerian D-algebras

Authors:
Mircea Sularia
Affiliations:
Department of Mathematics, Polytechnic University of Bucharest, Bucharest, Romania
Venue:
ISTASC'06 Proceedings of the 6th WSEAS International Conference on Systems Theory & Scientific Computation
Year:
2006

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Abstract

We introduced the structure of Brouwerian D-algebra in order to obtain the algebraic counterpart of a logic of problem solving. A Brouwerian D-algebra is defined by a subdirect product of a couple of algebras associated with a Heyting lattice and a Brouwer lattice. Then in this paper we introduce the notion of involutive Brouwerian D-algebra having as models direct products between the lattice of open sets and the lattice of closed sets of a topological space. Different properties including basic distributivity equations for complete Brouwerian D-algebras are presented. An extension of the real graded membership space for fuzzy sets is obtained. A connection with the notion of prelinear Heyting MV-algebra is also established.