Studying sequent systems via non-deterministic multiple-valued matrices

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We consider a family of sequent systems with "well-behaved" logical rules in which the cut rule and/or the identity-axiom are not present. We provide a semantic characterization of the logics induced by these systems in the form of non-deterministic three-valued or four-valued matrices. The semantics is used to study some important proof-theoretic properties of these systems. These results shed light on the dual semantic roles of the cut rule and the identity-axiom, showing that they are both crucial for having deterministic finite-valued semantics.

Original languageEnglish
Pages (from-to)575-595
Number of pages21
JournalJournal of Multiple-Valued Logic and Soft Computing
Issue number5-6
StatePublished - 2013


  • Cut-elimination
  • Multiple-valued logics
  • Non-deterministic semantics
  • Proof theory
  • Semantic proofs
  • Sequent systems


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