Computations in Boolean Algebra with Approximation

Article type: Research Article

Authors: Kostanyan, Armen | Khnkoyan, Paruyr

Affiliations: Educational and Research Center of Information Technologies, Yerevan State University, Alex Manoogian 1, 0025 Yerevan, Armenia. armko@ysu.am | Educational and Research Center of Information Technologies, Yerevan State University, Yerevan, Armenia

Note: [] Address for correspondence: Alex Manoogian 1, 0025 Yerevan, Armenia

Abstract: 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.

Keywords: Lukasiewicz three-valued logic, Boolean algebra, approximative computations

DOI: 10.3233/FI-2014-1120

Journal: Fundamenta Informaticae, vol. 135, no. 3, pp. 229-241, 2014