Home // International Journal On Advances in Intelligent Systems, volume 11, numbers 1 and 2, 2018 // View article

Deduction System for Decision Logic Based on Many-valued Logics

Authors:
Yotaro Nakayama
Seiki Akama
Tetsuya Murai

Keywords: rough set; decision logic; consequence relation; many-valued logic; sequent calculi.

Abstract:
Rough set theory has been extensively used both as a mathematical foundation of granularity and vagueness in information systems and in a large number of applications. However, the decision logic for rough sets is based on classical bivalent logic; therefore, it would be desirable to develop decision logic for uncertain, ambiguous and inconsistent objects. In this study, a deduction system based on partial semantics is proposed for decision logic. We propose Belnap's four-valued semantics as the basis for three-valued and four-valued logics to extend the deduction of decision logic since the boundary region of rough sets is interpreted as both a non-deterministic and inconsistent state. We also introduce the consequence relations to serve as an intermediary between rough sets and many-valued semantics. Hence, consequence relations based on partial semantics for decision logic are defined, and axiomatization by Gentzen-type sequent calculi is obtained. Furthermore, we extend the sequent calculi with a weak implication to hold for a deduction theorem and also show a soundness and completeness theorem for the four-valued logic for decision logic.

Pages: 115 to 126

Copyright: Copyright (c) to authors, 2018. Used with permission.

Publication date: June 30, 2018

Published in: journal

ISSN: 1942-2679