Game theoretical semantics for some non-classical logics

Can Baskent

Research output: Contribution to journalArticle

2 Citations (Scopus)
122 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)208-239
Number of pages32
JournalJournal of Applied Non-Classical Logics
Volume26
Issue number3
DOIs
Publication statusPublished - 2 Sep 2016

Keywords

  • Belnap’s four-valued logic B4
  • connexive logic
  • first-degree entailment
  • Game theoretical semantics
  • logic of paradox
  • modal logic S5
  • relevant logic

ASJC Scopus subject areas

  • Logic
  • Philosophy

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