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Non-Deterministic Semantics for Logical Systems

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Handbook of Philosophical Logic

Part of the book series: Handbook of Philosophical Logic ((HALO,volume 16))

Abstract

The principle of truth-functionality (or compositionality) is a basic principle in many-valued logic in general, and in classical logic in particular. According to this principle, the truth-value of a complex formula is uniquely determined by the truth-values of its subformulas. However, real-world information is inescapably incomplete, uncertain, vague, imprecise or inconsistent, and these phenomena are in an obvious conflict with the principle of truth-functionality. One possible solution to this problem is to relax this principle by borrowing from automata and computability theory the idea of non-deterministic computations, and apply it in evaluations of truth-values of formulas. This leads to the introduction of non-deterministic matrices (Nmatrices) — a natural generalization of ordinary multi-valued matrices, in which the truth-value of a complex formula can be chosen nondeterministically out of some non-empty set of options. There are many natural motivations for introducing non-determinism into the truth-tables of logical connectives.

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  1. Tel-Aviv University, Tel-Aviv, Israel

    Arnon Avron & Anna Zamansky

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  1. Arnon Avron
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  2. Anna Zamansky
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Correspondence to Arnon Avron .

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  1. Dept. Computer Science, King's College London, London, WC2R 2LS, United Kingdom

    Dov M. Gabbay

  2. , Centrüm für Informations- und Sprachvera, University of Munich, Oettingenstr. 67, Munich, 80538, Germany

    Franz Guenthner

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Avron, A., Zamansky, A. (2011). Non-Deterministic Semantics for Logical Systems. In: Gabbay, D., Guenthner, F. (eds) Handbook of Philosophical Logic. Handbook of Philosophical Logic, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0479-4_4

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