A formal logical system dealing with both uncertainty (possibility) and vagueness (fuzziness) is investigated. It is many-valued and modal. The system is related to a many-valued tense logic. A completeness theorem is exhibited. K E Y W O R D S : fuzzy logic, modal logic, possibilistic logic, comparative approach

Using the lattice-theoretic version of the Euler characteristic introduced by V. Klee and G.-C. Rota in the Sixties, we define the Euler characteristic of a formula in Gödel logic (over finitely or infinitely many truth-values). We then prove that the information encoded by the Euler characteristic is classical, i.e. coincides with the analogous notion defined over Boolean logic. Building on th...

We look at extensions (i.e., stronger logics in the same language) of the Belnap-Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap-Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterize the reduced algebraic models of these new logics and prove a completeness result for the first ...

We propose a new definition of the representation theorem for many-valued logics, with modal operators as well, and define the stronger relationship between algebraic models of a given logic and relational structures used to define the Kripke possible-world semantics for it. Such a new framework offers a new semantics for many-valued logics based on the truth-invariance entailment. Consequently...

Abstract We translate the three-valued quantum logic into modal logic, and prove 3-equivalence between valuation of a kind Kripke model in regard to this translation. To 3-equivalence, we introduce an observable-dependent which is fragment many-valued logic. Compared Birkhoff von Neumann’s some notions about observables, completeness relation for example, mechanics can be utilized if employed.

We present a method for testing the validity for any finite manyvalued logic by using simple transformations into the validity problem for von Wright’s logic of elsewhere. The method provides a new original viewpoint on finite many-valuedness. Indeed, we present a uniform modal encoding of any finite many-valued logic that views truth-values as nominals. Improvements of the transformations are ...

Many-valued models, besides providing a natural semantical interpretation for several non-classical logics, constitute a very sharp tool for investigating and understanding meta-logical properties in general. Although open to debates from the philosophical perspective, seen from the mathematical viewpoint many-valued matrices and algebras are perfectly well-defined mathematical objects with sev...