• Corpus ID: 250072279

Frame definability in finitely-valued modal logics

  title={Frame definability in finitely-valued modal logics},
  author={Guillermo Badia and Xavier Caicedo and Carles Noguera},
In this paper we study frame definability in finitely-valued modal logics and establish two main results via suitable translations: (1) in finitely-valued modal logics one cannot define more classes of frames than are already definable in classical modal logic (cf. [28, Thm. 8]), and (2) a large family of finitely-valued modal logics define exactly the same classes of frames as classical modal logic (including modal logics based on finite Heyting and MV -algebras, or even BL -algebras). In this way one… 
1 Citations

New foundations of reasoning via real-valued first-order logics

—Many-valued logics in general, and real-valued log- ics in particular, usually focus on a notion of consequence based on preservation of full truth, typical represented by the value 1 in the



Modal definability for Łukasiewicz validity relations

  • Studia Logica 104 (2): 343–363
  • 2016

Possible worlds and many truth values

Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism

In order to prove the validity of logical rules, one has to assume these rules in the metalogic. However, rule-circular ‘justifications’ are demonstrably without epistemic value (sec. 1). Is a

Regular elements and Kolmogorov translation in residuated lattices

In this article, we study in detail the regular elements of a bounded, commutative and integral residuated lattice. We introduce the notion of a regular variety and explore its relationship with the

The Fregean Axiom and Polish mathematical logic in the 1920s

Summary of the talk given to the 22nd Conference on the History of Logic, Cracow (Poland), July 5–9, 1976.

Lattices and Ordered Algebraic Structures

Ordered sets residuated mappings.- Lattices lattice morphisms.- Regular equivalences.- Modular lattices.- Distributive lattices.- Complementation boolean algebras.- Pseudocomplementation Stone and


In his review (Kaplan [1966]) of the article in which Kripke first proposed his relational semantics for modal logic, David Kaplan posed the question: which properties of a binary relation are

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.