This paper examines truth diagrams for some non-classical, modal and dynamic logics. Truth diagrams are diagrammatic and visual ways to represent logical truth akin to truth tables, developed by Peter C.-H. Cheng. Currently, it is only given for classical propositional logic. In this paper, we establish truth diagrams for Priest's Logic of Paradox, Belnap–Dunn's Four-Valued Logic, MacColl's Connexive Logic, Bochvar–Halldén's Logic of Non-Sense, Carnielli–Coniglio's logic of formal inconsistency as well as classical modal logic and its dynamic extension to shed light (...) on the semantic behaviour of some non-classical and modal logics. (shrink)

We introduce game-theoretic semantics for systems without the conveniences of either a De Morgan negation, or of distribution of conjunction over disjunction and conversely. Much of game playing rests on challenges issued by one player to the other to satisfy, or refute, a sentence, while forcing him/her to move to some other place in the game’s chessboard-like configuration. Correctness of the game-theoretic semantics is proven for both a training game, corresponding to Positive Lattice Logic and for more advanced games for (...) the logics of lattices with weak negation and modal operators. (shrink)

This paper examines truth diagrams for some non-classical, modal and dynamic logics. Truth diagrams are diagrammatic and visual ways to represent logical truth akin to truth tables, developed by Peter C.-H. Cheng. Currently, it is only given for classical propositional logic. In this paper, we establish truth diagrams for Priest's Logic of Paradox, Belnap–Dunn's Four-Valued Logic, MacColl's Connexive Logic, Bochvar–Halldén's Logic of Non-Sense, Carnielli–Coniglio's logic of formal inconsistency as well as classical modal logic and its dynamic extension to shed light (...) on the semantic behaviour of some non-classical and modal logics. (shrink)

This is the Editorial Introduction to “S.I.: Strong and Weak Kleene Logics”.

Hintikka’s game theoretical approach to semantics has been successfully applied also to some non-classical logics. A recent example is Başkent (A game theoretical semantics for logics of nonsense, 2020. arXiv:2009.10878), where a game theoretical semantics based on three players and the notion of dominant winning strategy is devised to fit both Bochvar and Halldén’s logics of nonsense, which represent two basic systems of the family of weak Kleene logics. In this paper, we present and discuss a new game theoretic semantics (...) for Bochvar and Halldén’s logics, GTS-2, and show how it generalizes to a broader family of logics of variable inclusions. (shrink)

This paper examines truth diagrams for some non-classical, modal and dynamic logics. Truth diagrams are diagrammatic and visual ways to represent logical truth akin to truth tables, developed by Peter C.-H. Cheng. Currently, it is only given for classical propositional logic. In this paper, we establish truth diagrams for Priest's Logic of Paradox, Belnap–Dunn's Four-Valued Logic, MacColl's Connexive Logic, Bochvar–Halldén's Logic of Non-Sense, Carnielli–Coniglio's logic of formal inconsistency as well as classical modal logic and its dynamic extension to shed light (...) on the semantic behaviour of some non-classical and modal logics. (shrink)