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