Deduction System for Decision Logic based on Partial Semantics

摘要

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 or ambiguous objects. In this study, a deduction system based on partial semantics is proposed for decision logic. Three-valued logics based on Gentzen sequent calculi are adopted. A deductive system based on three-valued framework is intuitively adequate for the structure of positive, negative, and boundary regions of rough sets, and has already been studied. In this study, consequence relations based on partial semantics for decision logic are defined, and systemization by Gentzen's sequent calculi is attempted. Three-valued logics of different structures are investigated as the deductive system of decision logic. The interpretation of decision logic is extended using partial semantics, and extended decision logic based on three-valued logics is proposed.