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Toward a general frame semantics for modal many-valued logics.
- Source :
-
Soft Computing - A Fusion of Foundations, Methodologies & Applications . Apr2019, Vol. 23 Issue 7, p2233-2241. 9p. - Publication Year :
- 2019
-
Abstract
- Frame semantics, given by Kripke or neighborhood frames, do not give completeness theorems for all modal logics extending, respectively, K and E. Such shortcoming can be overcome by means of general frames, i.e., frames equipped with a collection of admissible sets of worlds (which is the range of possible valuations over such frame). We export this approach from the classical paradigm to modal many-valued logics by defining general A-frames over a given residuated lattice A (i.e., the usual frames with a collection of admissible A-valued sets). We describe in detail the relation between general Kripke and neighborhood A-frames and prove that, if the logic of A is finitary, all extensions of the corresponding logic E of A are complete w.r.t. general neighborhood frames. Our work provides a new approach to the current research trend of generalizing relational semantics for non-classical modal logics to circumvent axiomatization problems. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MODAL logic
*MANY-valued logic
*GENERAL semantics
*SEMANTICS
Subjects
Details
- Language :
- English
- ISSN :
- 14327643
- Volume :
- 23
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Soft Computing - A Fusion of Foundations, Methodologies & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 135412228
- Full Text :
- https://doi.org/10.1007/s00500-018-3369-5