Operational Semantics for Positive Relevant Logics Without Distribution

  • Authors:

  • Ying Gao;Jingde Cheng

  • Affiliations:

  • Department of Information and Computer Sciences, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama, 338-8570, Japan;Department of Information and Computer Sciences, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama, 338-8570, Japan

  • Venue:
  • CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
  • Year:
  • 2007

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Abstract

This paper investigates operational semantics for variouspositive relevant logics without distribution after the work of KitFine in Models for Entailment. To invalidate the law ofdistribution of conjunction over disjunction, we use differenttypes of states to model conjunction and disjunction, respectively.The implication → is interpreted by three operations ⊕ ,⊗ , ⊖, instead of one operation `·' as inFine's work.