Quantification in non-deterministic multi-valued structures

Arnon Avron, Anna Zamansky

Research output: Contribution to journalConference articlepeer-review


In this paper the concept of a multi-valued non-deterministic (prepositional) matrix, in which non-deterministic computations of truth values are allowed, is extended to languages with quantifiers. We describe the difficulties involved in applying the two main classical approaches to interpreting quantifiers, the objectual and the substitutional, and solve the difficulties in the case of the latter. Then we turn to the two-valued case, and explore the effects in this context of each of the four standard Gentzen-type rules for the classical quantifiers. As an example, a sound and complete two-valued non-deterministic semantics is provided for a family of first-order proof systems.

Original languageEnglish
Pages (from-to)296-301
Number of pages6
JournalProceedings of The International Symposium on Multiple-Valued Logic
StatePublished - 2005
Externally publishedYes
Event35th International Symposium on Multiple-Valued Logic, ISMVL 2005 - Calgary, Alta., Canada
Duration: 19 May 200521 May 2005

ASJC Scopus subject areas

  • General Computer Science
  • General Mathematics


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