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Finite-valued Semantics for Canonical Labelled Calculi

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Abstract

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.

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Authors and Affiliations

  1. Vienna University of Technology, Wien, Austria

    Matthias Baaz & Anna Zamansky

  2. Tel Aviv University, Tel Aviv, Israel

    Ori Lahav

Authors
  1. Matthias Baaz
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  2. Ori Lahav
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  3. Anna Zamansky
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Corresponding author

Correspondence to Ori Lahav.

Additional 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.

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Baaz, M., Lahav, O. & Zamansky, A. Finite-valued Semantics for Canonical Labelled Calculi. J Autom Reasoning 51, 401–430 (2013). https://doi.org/10.1007/s10817-013-9273-x

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  • DOI: https://doi.org/10.1007/s10817-013-9273-x

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