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Computations in Boolean Algebra with Approximation

Kostanyan A., Khnkoyan P.

Fundamenta Informaticae

2014

Vol. 135, nr 3

229--241

Computations in Boolean algebra extended by adding an undefined element are investigated in the present paper. These computations (also known as approximative computations) are based on Lukasiewicz three-valued logic and are widely used in those applications where it is necessary to perform logical operations under uncertainty. The approximative computations are carried out as follows: if all instantiations of undefined operands produce the same result then this ascertained result is taken as final; otherwise, the final result is defined to be unknown. The key question in theory of approximative computations is whether a given Boolean formula is closed in the sense that the stepwise approximative computations in compliance with a given formula produce a result as accurate as possible. This question is investigated for the classes of disjunctive and algebraic normal forms.

About Two Different Ways of Characterization of Łuksiewicz's Three-valued Modal Propositional Calculus

Bryll G., Kaptur M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2005

Vol. 10

25-31

In this article we consider two systems of Lukasiewicz's three- valued modal propositional calculus. One of them is the system based on such primary terms as the disjunction (A), negation (N) and necessity (L), whereas the second is based on such primary terms as the implication (C), negation (N) and definitively improved by modal necessity terms. The both systems are definitively equivalent.