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Non-deterministic Matrices and Modular Semantics of Rules

In: Logica Universalis

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  • Arnon Avron

    (Tel-Aviv University, School of Computer Science)

Abstract

We show by way of example how one can provide in a lot of cases simple modular semantics of rules of inference, so that the semantics of a system is obtained by joining the semantics of its rules in the most straightforward way. Our main tool for this task is the use of finite Nmatrices, which are multi-valued structures in which the value assigned by a valuation to a complex formula can be chosen non-deterministically out of a certain nonempty set of options. The method is applied in the area of logics with a formal consistency operator (knowns as LFIs), allowing us to provide in a modular way effective, finite semantics for thousands of different LFIs.

Suggested Citation

  • Arnon Avron, 2005. "Non-deterministic Matrices and Modular Semantics of Rules," Springer Books, in: Jean-Yves Beziau (ed.), Logica Universalis, pages 149-167, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7643-7304-7_9
    DOI: 10.1007/3-7643-7304-0_9
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