Kripke Semantics for Fuzzy Logics

Soft Computing 22 (3):839–844 (2018)
  Copy   BIBTEX

Abstract

Kripke frames (and models) provide a suitable semantics for sub-classical logics; for example, intuitionistic logic (of Brouwer and Heyting) axiomatizes the reflexive and transitive Kripke frames (with persistent satisfaction relations), and the basic logic (of Visser) axiomatizes transitive Kripke frames (with persistent satisfaction relations). Here, we investigate whether Kripke frames/models could provide a semantics for fuzzy logics. For each axiom of the basic fuzzy logic, necessary and sufficient conditions are sought for Kripke frames/models which satisfy them. It turns out that the only fuzzy logics (logics containing the basic fuzzy logic) which are sound and complete with respect to a class of Kripke frames/models are the extensions of the Gödel logic (or the super-intuitionistic logic of Dummett); indeed this logic is sound and strongly complete with respect to reflexive, transitive and connected (linear) Kripke frames (with persistent satisfaction relations). This provides a semantic characterization for the Gödel logic among (propositional) fuzzy logics.

Links

PhilArchive

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Kripke-style semantics for many-valued logics.Franco Montagna & Lorenzo Sacchetti - 2003 - Mathematical Logic Quarterly 49 (6):629.
Linear Kripke Frames and Gödel Logics.Arnold Beckmann & Norbert Preining - 2007 - Journal of Symbolic Logic 72 (1):26 - 44.
A Closer Look at Some Subintuitionistic Logics.Ramon Jansana & Sergio Celani - 2001 - Notre Dame Journal of Formal Logic 42 (4):225-255.
A Closer Look at Some Subintuitionistic Logics.Sergio Celani & Ramon Jansana - 2001 - Notre Dame Journal of Formal Logic 42 (4):225-255.
Properties of Tense Logics.Frank Wolter - 1996 - Mathematical Logic Quarterly 42 (1):481-500.
Kripke bundle semantics and c-set semantics.Eiko Isoda - 1997 - Studia Logica 58 (3):395-401.
Tense Logic Without Tense Operators.Frank Wolter - 1996 - Mathematical Logic Quarterly 42 (1):145-171.
Rudimentary Kripke models for the intuitionistic propositional calculus.Kosta Došen - 1993 - Annals of Pure and Applied Logic 62 (1):21-49.
Barwise's information frames and modal logics.Vladimir V. Rybakov - 2003 - Archive for Mathematical Logic 42 (3):261-277.

Analytics

Added to PP
2021-02-21

Downloads
291 (#63,592)

6 months
85 (#44,038)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Saeed Salehi
University of Tabriz

Citations of this work

Avicenna on Syllogisms Composed of Opposite Premises.Behnam Zolghadr - 2021 - In Mojtaba Mojtahedi, Shahid Rahman & MohammadSaleh Zarepour (eds.), Mathematics, Logic, and their Philosophies: Essays in Honour of Mohammad Ardeshir. Springer. pp. 433-442.

Add more citations

References found in this work

No references found.

Add more references