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REDUCTION TECHNIQUES FOR PROVING DECIDABILITY IN LOGICS AND THEIR MEET–COMBINATION

Part of: General logic

Published online by Cambridge University Press:  06 May 2021

JOÃO RASGA ,
CRISTINA SERNADAS  and
WALTER CARNIELLI
JOÃO RASGA
Affiliation:
DEPARTAMENTO DE MATEMÁTICA INSTITUTO SUPERIOR TÉCNICO UNIVERSIDADE DE LISBOA, LISBOA, PORTUGALE-mail: joao.rasga@tecnico.ulisboa.ptURL: https://fenix.tecnico.ulisboa.pt/homepage/ist14184
CRISTINA SERNADAS
Affiliation:
INSTITUTO DE TELECOMUNICAÇÕESLISBOA, PORTUGALE-mail: cristina.sernadas@tecnico.ulisboa.ptURL: https://fenix.tecnico.ulisboa.pt/homepage/ist12466
WALTER CARNIELLI
Affiliation:
CENTRE FOR LOGIC EPISTEMOLOGY AND THE HISTORY OF SCIENCE UNIVERSITY OF CAMPINAS—UNICAMP, CAMPINAS, BRAZILE-mail: walterac@unicamp.brURL: https://www.cle.unicamp.br/prof/carnielli/
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Abstract

Satisfaction systems and reductions between them are presented as an appropriate context for analyzing the satisfiability and the validity problems. The notion of reduction is generalized in order to cope with the meet-combination of logics. Reductions between satisfaction systems induce reductions between the respective satisfiability problems and (under mild conditions) also between their validity problems. Sufficient conditions are provided for relating satisfiability problems to validity problems. Reflection results for decidability in the presence of reductions are established. The validity problem in the meet-combination is proved to be decidable whenever the validity problem for the components are decidable. Several examples are discussed, namely, involving modal and intuitionistic logics, as well as the meet-combination of $\textrm {K}$ modal logic and intuitionistic logic.

Keywords

meet-combination of logicsreductiondecidability

MSC classification

Primary: 03B25: Decidability of theories and sets of sentences
Secondary: 03B45: Modal logic (including the logic of norms) 03B62: Combined logics
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 27 , Issue 1 , March 2021 , pp. 39 - 66
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Copyright
© The Association for Symbolic Logic 2021

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