Finite-valued semantics for canonical labelled calculi

Matthias Baaz, Ori Lahav, Anna Zamansky

Research output: Contribution to journalArticlepeer-review


We define a general family of canonical labelled calculi, of which many previously studied sequent and labelled calculi are particular instances. We then provide a uniform and modular method to obtain finite-valued semantics for every canonical labelled calculus by introducing the notion of partial non-deterministic matrices. The semantics is applied to provide simple decidable semantic criteria for two crucial syntactic properties of these calculi: (strong) analyticity and cut-admissibility. Finally, we demonstrate an application of this framework for a large family of paraconsistent logics.

Original languageEnglish
Pages (from-to)401-430
Number of pages30
JournalJournal of Automated Reasoning
Issue number4
StatePublished - Dec 2013
Externally publishedYes

Bibliographical note

Funding Information:
The second author is supported by The Israel Science Foundation (grant no. 280-10) and by FWF START Y544-N23. The third author is supported by The European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 252314.


  • Canonical calculi
  • Cut-admissibility
  • Finite-valued logics
  • Labelled sequents
  • Non-deterministic semantics
  • Sequent calculi

ASJC Scopus subject areas

  • Software
  • Computational Theory and Mathematics
  • Artificial Intelligence


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