Finite-valued semantics for canonical labelled calculi

Matthias Baaz, Ori Lahav*, Anna Zamansky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


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


FundersFunder number
Seventh Framework Programme252314
Austrian Science FundSTART Y544-N23
Israel Science Foundation280-10


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


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