Journal of Philosophical Logic

, Volume 32, Issue 5, pp 483–529 | Cite as

Neighborhoods for Entailment

  • Lou Goble


This paper presents a neighborhood semantics for logics of entailment. It begins with a minimal system Min that expresses the most fundamental assumptions about the entailment relation, and continues by examining various extensions that reflect further assumptions that might be made about entailment. This leads first to the logic B that is the basic relevant logic, and then to more powerful systems. All of these logics are proved to be sound and strongly complete. With B the neighborhood semantics meets the Routley–Meyer relational semantics for relevant logic; these connections are examined. The minimal and basic entailment logics are shown to have the finite model property, and hence to be decidable.

entailment implication neighborhood semantics relevance logic substructural logic 


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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Lou Goble
    • 1
  1. 1.Department of PhilosophyWillamette UniversitySalemUSA

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