Measuring inconsistency in some branching time logics

Abstract

Branching time logics have been studied in computer science since the 1980s primarily to model the tree of computations for discrete transition systems. Inconsistency measures for propositional logic have been studied since the early 2000s by AI researchers. This paper introduces inconsistency measures for three branching time logics: ABTL, BBTL, and CBTL. In order to measure inconsistency properly in branching time logics, the semantics differs from the standard semantics using the construction of a canonical tree. ABTL extends propositional logic by three pairs of unary operators: next time, path, and eventually. BBTL adds a pair of binary Until operators that can be applied only to propositional logic formulas. CBTL adds the propositional connectives to BBTL formulas. Propositional logic inconsistency measures are extended to these logics and examples of the computation are given. These measures are shown to satisfy intuitively the concepts involved in the branching time logic operators unlike direct extensions of propositional logic inconsistency measures.