Non-deterministic matrices for semi-canonical deduction systems

Ori Lahav

doi:10.1109/ISMVL.2012.48

Non-deterministic matrices for semi-canonical deduction systems

Ori Lahav^*

^*Corresponding author for this work

School of Computer Science

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

3 Scopus citations

Abstract

We use non-deterministic finite-valued matrices to provide uniform effective semantics for a large family of logics, emerging from "well-behaved" sequent systems in which the cut rule and/or the identity-axiom are not present. We exploit this semantics to obtain important proof-theoretic properties of systems of this kind, such as cut-admissibility. Non-determinism is shown to be essential for these purposes, since the studied logics cannot be characterized by ordinary finite-valued matrices. Our results shed light on the dual semantic roles of the cut rule and the identity-axiom, showing that they are crucial for having deterministic (truth-functional) finite-valued semantics.

Original language	English
Title of host publication	Proceedings - IEEE 42nd International Symposium on Multiple-Valued Logic, ISMVL 2012
Pages	79-84
Number of pages	6
DOIs	https://doi.org/10.1109/ISMVL.2012.48
State	Published - 2012
Event	42nd IEEE International Symposium on Multiple-Valued Logic, ISMVL 2012 - Victoria, BC, Canada Duration: 14 May 2012 → 16 May 2012

Publication series

Name	Proceedings of The International Symposium on Multiple-Valued Logic
ISSN (Print)	0195-623X

Conference

Conference	42nd IEEE International Symposium on Multiple-Valued Logic, ISMVL 2012
Country/Territory	Canada
City	Victoria, BC
Period	14/05/12 → 16/05/12

Access to Document

10.1109/ISMVL.2012.48

Cite this

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title = "Non-deterministic matrices for semi-canonical deduction systems",

abstract = "We use non-deterministic finite-valued matrices to provide uniform effective semantics for a large family of logics, emerging from {"}well-behaved{"} sequent systems in which the cut rule and/or the identity-axiom are not present. We exploit this semantics to obtain important proof-theoretic properties of systems of this kind, such as cut-admissibility. Non-determinism is shown to be essential for these purposes, since the studied logics cannot be characterized by ordinary finite-valued matrices. Our results shed light on the dual semantic roles of the cut rule and the identity-axiom, showing that they are crucial for having deterministic (truth-functional) finite-valued semantics.",

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Lahav, O 2012, Non-deterministic matrices for semi-canonical deduction systems. in Proceedings - IEEE 42nd International Symposium on Multiple-Valued Logic, ISMVL 2012., 6214787, Proceedings of The International Symposium on Multiple-Valued Logic, pp. 79-84, 42nd IEEE International Symposium on Multiple-Valued Logic, ISMVL 2012, Victoria, BC, Canada, 14/05/12. https://doi.org/10.1109/ISMVL.2012.48

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Non-deterministic matrices for semi-canonical deduction systems

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