Semantics for a basic relevant logic with intensional conjunction and disjunction (and some of its extensions)

Authors:
Ying Gao;Jingde Cheng
Affiliations:
Department of information and computer sciences, saitama university, 255 shimo-okubo, sakura-ku, saitama, 338-8570, japan email: gaoying@aise.ics.saitama-u.ac.jp, cheng@aise.ics.saitama-u.ac.jp;Department of information and computer sciences, saitama university, 255 shimo-okubo, sakura-ku, saitama, 338-8570, japan email: gaoying@aise.ics.saitama-u.ac.jp, cheng@aise.ics.saitama-u.ac.jp
Venue:
Mathematical Structures in Computer Science
Year:
2008

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Abstract

This paper proposes a new relevant logicB+, which is obtained by adding two binary connectives,intensional conjunction and intensional disjunction , to MeyerRoutley minimal positive relevant logicB+, where and are weaker than fusion ° and fission +, respectively. We giveKripke-style semantics for B+, with ➝, and modelled by ternary relations. We prove the soundness andcompleteness of the proposed semantics. A number of axiomaticextensions of B+, including negation-extensions, are also considered,together with the corresponding semantic conditions required forsoundness and completeness to be maintained.