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.
Bibliographical noteFunding 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
- Finite-valued logics
- Labelled sequents
- Non-deterministic semantics
- Sequent calculi
ASJC Scopus subject areas
- Computational Theory and Mathematics
- Artificial Intelligence