Journal of Automated Reasoning

, Volume 51, Issue 4, pp 401–430 | Cite as

Finite-valued Semantics for Canonical Labelled Calculi

Article

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.

Keywords

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

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Vienna University of TechnologyWienAustria
  2. 2.Tel Aviv UniversityTel AvivIsrael

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