Non-deterministic matrices for semi-canonical deduction systems

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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 languageEnglish
Title of host publicationProceedings - IEEE 42nd International Symposium on Multiple-Valued Logic, ISMVL 2012
Number of pages6
StatePublished - 2012
Event42nd IEEE International Symposium on Multiple-Valued Logic, ISMVL 2012 - Victoria, BC, Canada
Duration: 14 May 201216 May 2012

Publication series

NameProceedings of The International Symposium on Multiple-Valued Logic


Conference42nd IEEE International Symposium on Multiple-Valued Logic, ISMVL 2012
CityVictoria, BC

All Science Journal Classification (ASJC) codes

  • General Computer Science
  • General Mathematics


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