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MODULAR MANY-VALUED SEMANTICS FOR COMBINED LOGICS

Part of: General logic

Published online by Cambridge University Press:  20 April 2023

CARLOS CALEIRO Open the ORCID record for CARLOS CALEIRO [Opens in a new window]  and
SÉRGIO MARCELINO Open the ORCID record for SÉRGIO MARCELINO [Opens in a new window]
CARLOS CALEIRO
Affiliation:
SQIG–INSTITUTO DE TELECOMUNICAÇÕES DEPARTAMENTO DE MATEMÁTICA INSTITUTO SUPERIOR TÉCNICO, UNIVERSIDADE DE LISBOA LISBOA, PORTUGAL E-mail: ccal@math.tecnico.ulisboa.pt
SÉRGIO MARCELINO*
Affiliation:
SQIG–INSTITUTO DE TELECOMUNICAÇÕES DEPARTAMENTO DE MATEMÁTICA INSTITUTO SUPERIOR TÉCNICO, UNIVERSIDADE DE LISBOA LISBOA, PORTUGAL E-mail: ccal@math.tecnico.ulisboa.pt
*
E-mail: smarcel@math.tecnico.ulisboa.pt
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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.

Keywords

modular semanticspartial non-deterministic logical matricesmultiple-conclusion logicmodularitycombined logicsfibring logicsadding axiomssplitting logicsdecidability preservation

MSC classification

Primary: 03B50: Many-valued logic
Secondary: 03B62: Combined logics
Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 54
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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