Quantification in non-deterministic multi-valued structures

Arnon Avron; Anna Zamansky

doi:10.1109/ISMVL.2005.40

Quantification in non-deterministic multi-valued structures

Arnon Avron^*, Anna Zamansky

^*Corresponding author for this work

School of Computer Science

Tel Aviv University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

17 Scopus citations

Abstract

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 language	English
Title of host publication	35th International Symposium on Multiple-Valued Logic (ISMVL'05)
Publisher	IEEE
Pages	296-301
Number of pages	6
ISBN (Print)	0-7695-2336-6
DOIs	https://doi.org/10.1109/ISMVL.2005.40
State	Published - 2005
Event	35th International Symposium on Multiple-Valued Logic, ISMVL 2005 - Calgary, Alta., Canada Duration: 19 May 2005 → 21 May 2005

Publication series

Name	Proceedings of The International Symposium on Multiple-Valued Logic
Publisher	IEEE Computer Society
ISSN (Print)	0195-623X
ISSN (Electronic)	2378-2226

Conference

Conference	35th International Symposium on Multiple-Valued Logic, ISMVL 2005
Country/Territory	Canada
City	Calgary, Alta.
Period	19/05/05 → 21/05/05

Access to Document

10.1109/ISMVL.2005.40

Cite this

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title = "Quantification in non-deterministic multi-valued structures",

abstract = "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.",

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Avron, A & Zamansky, A 2005, Quantification in non-deterministic multi-valued structures. in 35th International Symposium on Multiple-Valued Logic (ISMVL'05). Proceedings of The International Symposium on Multiple-Valued Logic, IEEE, pp. 296-301, 35th International Symposium on Multiple-Valued Logic, ISMVL 2005, Calgary, Alta., Canada, 19/05/05. https://doi.org/10.1109/ISMVL.2005.40

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Quantification in non-deterministic multi-valued structures

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