Measuring inconsistency in some logics with tense operators (Q2080703)

The paper presents a study of inconsistency measures for propositional tense logics in the standard Priorian language with tense operators: \(H\), \(G\), \(P\), and \(F\). The original idea of inconsistency measures for propositional logics goes back to a 1978 paper by the same author [Notre Dame J. Formal Logic 19, 435--444 (1978; Zbl 0305.02040)], and has since then been realised in different ways by several authors, briefly reviewed in the paper. The author introduces several measures of the inconsistency of a set of formulas of a given tense logic and then consider the satisfaction of natural properties, called rationality postulates, by each of these measures, thus evaluating the appropriateness of them. The paper also explores the connections between inconsistency measures and paraconsistent propositional tense logics.