Game theoretical semantics for some non-classical logics. Issue 3 (2nd July 2016)

• Record Type: Journal Article
• Authors: Başkent, Can
• Is Part Of: Journal of applied non-classical logics. Volume 26:Issue 3(2016)
• Page Start: 208
• Page End: 239
• Publication Date: 2016-07-02
• Subjects: Game theoretical semantics -- logic of paradox -- first-degree entailment -- relevant logic -- connexive logic -- Belnap's four-valued logic B4 -- modal logic S5; Nonclassical mathematical logic -- Periodicals; Wiskundige logica; Logic; Periodicals; 511.3105
• DOI: 10.1080/11663081.2016.1225488
• Languages: English
• ISSNs: 1166-3081

Abstract

Abstract : Paraconsistent logics are the formal systems in which absurdities do not trivialise the logic. In this paper, we give Hintikka-style game theoretical semantics for a variety of paraconsistent and non-classical logics. For this purpose, we consider Priest's Logic of Paradox, Dunn's First-Degree Entailment, Routleys' Relevant Logics, McCall's Connexive Logic and Belnap's four-valued logic. We also present a game theoretical characterisation of a translation between Logic of Paradox/Kleene's K3 and S5. We underline how non-classical logics require different verification games and prove the correctness theorems of their respective game theoretical semantics. This allows us to observe that paraconsistent logics break the classical bidirectional connection between winning strategies and truth values.