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arXiv · 2202.02189

Modular many-valued semantics for combined logics

Carlos Caleiro·Sérgio Marcelino
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Abstract

We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic logical matrices. Our constructions preserve finite-valuedness in the context of multiple-conclusion logics whereas, unsurprisingly, it may be lost in the context of single-conclusion logics. Besides illustrating our constructions over a wide range of examples, we also develop concrete applications of our semantic characterizations, namely regarding the semantics of strengthening a given many-valued logic with additional axioms, the study of conditions under which a given logic may be seen as a combination of simpler syntactically defined fragments whose calculi can be obtained independently and put together to form a calculus for the whole logic, and also general conditions for decidability to be preserved by the combination mechanism.

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Carlos Caleiro, Sérgio Marcelino. 2022-02-04. Modular many-valued semantics for combined logics. https://doi.org/10.1017/jsl.2023.22

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