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Preservation of admissible rules when combining logics

João Rasga, Cristina Sernadas & Amílcar Sernadas

Review of Symbolic Logic 9 (4):641-663 (2016)

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Reduction Techniques for Proving Decidability in Logics and Their Meet–Combination.João Rasga, Cristina Sernadas & Walter Carnielli - 2021 - Bulletin of Symbolic Logic 27 (1):39-66.details 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 (...) Download Export citation Bookmark 1 citation
Essential Structure of Proofs as a Measure of Complexity.Jaime Ramos, João Rasga & Cristina Sernadas - 2020 - Logica Universalis 14 (2):209-242.details The essential structure of proofs is proposed as the basis for a measure of complexity of formulas in FOL. The motivating idea was the recognition that distinct theorems can have the same derivation modulo some non essential details. Hence the difficulty in proving them is identical and so their complexity should be the same. We propose a notion of complexity of formulas capturing this property. With this purpose, we introduce the notions of schema calculus, schema derivation and description complexity of (...) Download Export citation Bookmark
Combining logics.Walter Carnielli & Marcelo E. Coniglio - 2008 - Stanford Encyclopedia of Philosophy.details Although a very recent topic in contemporary logic, the subject of combinations of logics has already shown its deep possibilities. Besides the pure philosophical interest offered by the possibility of defining mixed logic systems in which distinct operators obey logics of different nature, there are also several pragmatical and methodological reasons for considering combined logics. We survey methods for combining logics (integration of several logic systems into a homogeneous environment) as well as methods for decomposing logics, showing their interesting properties (...) and applications. (shrink) Download Export citation Bookmark 5 citations

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