Non-deterministic matrices and modular semantics of rules

Arnon Avron*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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.

Original languageEnglish
Title of host publicationLogica Universalis
Subtitle of host publicationTowards a General Theory of Logic
PublisherBirkhäuser Basel
Number of pages19
ISBN (Print)9783764383534
StatePublished - 2007


  • Propositional logics
  • multiple-valued semantics
  • paraconsistency


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