On modal extensions of Product fuzzy logic

  title={On modal extensions of Product fuzzy logic},
  author={Amanda Vidal and Francesc Esteva and Llu{\'i}s Godo},
  journal={J. Log. Comput.},
The authors wish to thank the anonymous reviewers for their valuable comments and suggestions that have significantly improved the article. They also thank Felix Bou and Tommaso Moraschini for helpful comments on Section 5. The authors acknowledge support of the Spanish projects EdeTRI (TIN2012-39348- C02-01) and 2014 SGR 118. Vidal was supported by a CSIC grant JAE Predoc. 

An alternative axiomatization for a fuzzy modal logic of preferences

This paper proposes an alternative axiomatic system with a multi-modal language, where the original modal operators are definable and their semantics are preserved, and for which completeness results are proved.

Paraconsistent Logic with Multiple Fuzzy Linguistic Truth-values

The two-valued paraconsistent logic is extended into an one in which a proposition takes a truth-value from a set of multiple fuzzy linguistic terms, and the corresponding inference rule and semantics are proposed.

From Fuzzy Sets to Mathematical Fuzzy Logic

In this paper our aim is to provide a short survey of main historical developments of systems of fuzzy logic in narrow sense, today under the umbrella of the discipline called Mathematical Fuzzy

On modal expansions of t-norm based logics with rational constants

The main goal of this thesis has been to study modal expansions of the logic of a left-continuous t-norm, defined over the language of MTL expanded with rational truth-constants and the Monteiro-Baaz Delta-operator, and to develop and automated reasoning software tool to solve satisfiability and logical consequence problems for some of the fuzzy logic modal logics considered.

A Multi-linguistic-Valued Modal Logic

This paper develops a multi-valued modal logic, in which a logic formula takes a value of truth in linguistic terms and its values are linguistic terms, which can be modelled as fuzzy sets.

An Approach to Fuzzy Modal Logic of Time Intervals

A fuzzy generalization of HS is presented that partially solves problems of expressive power, and it is proved that, as in the crisp case, its satisfiability problem is generally undecidable.

A modal extension of the solver NiBLos

mNiBLoS (a modal Nice BL-Logics Solver): a modular SMT-based solver complete with respect to a wide family of continuous t-norm based fuzzy modal logics (both with finite and infinite universes), restricting the modal structures to the finite ones.

Some Epistemic Extensions of G\"odel Fuzzy Logic

Some epistemic extensions of G¨odel fuzzy logic whose Kripke-based semantics have fuzzy values for both propositions and accessibility relations such that soundness and completeness hold.



Metamathematics of Fuzzy Logic

  • P. Hájek
  • Philosophy, Computer Science
    Trends in Logic
  • 1998
This paper presents a meta-analysis of many-Valued Propositional Logic, focusing on the part of Lukasiewicz's Logic that deals with Complexity, Undecidability and Generalized Quantifiers and Modalities.

On fuzzy modal logics S5(L)

  • P. Hájek
  • Computer Science
    Fuzzy Sets Syst.
  • 2010

Extending possibilistic logic over Gödel logic

About axiomatic systems of product fuzzy logic

It is proved that there cannot be any axiomatic system of the product fuzzy logic with single non-BL axiom with only one variable.

Residuated logics based on strict triangular norms with an involutive negation

This work studies several equations which are satisfied by some strict t-norms and their dual t-conorms and adds an involutive negation, which allows it to generate countably many logics based on strict t -norms which are different from the product logic.

A complete many-valued logic with product-conjunction

A simple complete axiomatic system is presented for the many-valued propositional logic based on the conjunction interpreted as product, the coresponding implication (Goguen's implication) and the

On Weakly Cancellative Fuzzy Logics

The weak cancellation property is proved to be the difference between cancellation and pseudocomplementation, so it gives a new axiomatization of product logic and ΠMTL.

A Finite Model Property for Gödel Modal Logics

A new semantics with the finite model property is provided and used to establish decidability for Godel modal logics based on crisp or fuzzy Kripke frames combined locally with Godel logic. A similar