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Theory matrices (for modal logics) using alphabetical monotonicity
- Source :
- Studia Logica. 52:233-257
- Publication Year :
- 1993
- Publisher :
- Springer Science and Business Media LLC, 1993.
-
Abstract
- In this paper I give conditions under which a matrix characterisation of validity is correct for first order logics where quantifications are restricted by statements from a theory. Unfortunately the usual definition of path closure in a matrix is unsuitable and a less pleasant definition must be used. I derive the matrix theorem from syntactic analysis of a suitable tableau system, but by choosing a tableau system for restricted quantification I generalise Wallen's earlier work on modal logics. The tableau system is only correct if a new condition I call “alphabetical monotonicity” holds. I sketch how the result can be applied to a wide range of logics such as first order variants of many standard modal logics, including non-serial modal logics.
- Subjects :
- Discrete mathematics
Logic
Normal modal logic
Algebra
Matrix (mathematics)
TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES
Modal
History and Philosophy of Science
Closure (mathematics)
Computer Science::Logic in Computer Science
Monoidal t-norm logic
Accessibility relation
Kripke semantics
T-norm fuzzy logics
Mathematics
Subjects
Details
- ISSN :
- 15728730 and 00393215
- Volume :
- 52
- Database :
- OpenAIRE
- Journal :
- Studia Logica
- Accession number :
- edsair.doi...........c274118d3bc4ed9b1ad738e381fdcc0e