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Logica Universalis pp 155–173Cite as

Non-deterministic Matrices and Modular Semantics of Rules

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Abstract

We show by way of example how one can provide in a lot of cases simple modular semantics for rules of inference, so that the semantics of a system is obtained by joining the semantics of its rules in the most straight-forward way. Our main tool for this task is the use of finite matrices, 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 (known as LFIs), allowing us to provide in a modular way effective, finite semantics for thousands of different LFIs.

This research was supported by THE ISRAEL SCIENCE FOUNDATION founded by The Israel Academy of Sciences and Humanities.

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Author information

Authors and Affiliations

  1. School of Computer Science, Tel-Aviv University, Ramat Aviv, 69978, Israel

    Arnon Avron

Authors
  1. Arnon Avron
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Editor information

Editors and Affiliations

  1. Swiss National Science Foundation, University of Neuchâtel, Espace Louis Agassiz 1, 2000, Neuchâtel, Switzerland

    Jean-Yves Beziau

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Avron, A. (2007). Non-deterministic Matrices and Modular Semantics of Rules. In: Beziau, JY. (eds) Logica Universalis. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8354-1_9

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