Multi-valued logics can be effectively used to reason about incomplete and/or inconsistent systems, e.g. during early software requirements or as the systems evolve. In our earlier work we identified a useful family of multi-valued logics: those specified over finite distributive lattices where negation preserves involution, i.e., , , -/.0for every element of the logic. Model-checking over this...

Two families of many-valued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite many-valued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds also to be many-valued. Gentzen sequent calculi are given for both versions, and soundness and compl...

2 General theory 3 2.1 Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Some logical calculi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 Sequent and tableau calculi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.2 Resolution calculi . . . . . . . . . . . . . . . . . . . . . ...

We present two complex valued probabilistic logics, LCOMPB and LCOMPS , which extend classical propositional logic. In LCOMPB one can express formulas of the form Bz,ρα meaning that the probability of α is in the complex ball with the center z and the radius ρ, while in LCOMPS one can make statements of the form Sz,ρα with the intended meaning – the probability of propositional formula α is in ...

We claim that Proof Systems for natural many-valued logics, whether nite-valued or innnite-valued should be similar in their structure to proof systems of any other natural logic: one should not be able to tell from the structures which are used in a proof system the intended semantics. It is also preferable that standard connectives will be used, with corresponding standard rules. We demonstra...

There are several three-valued logical systems that form a scattered landscape, even if all reasonable connectives in three-valued logics can be derived from a few of them. Most papers on this subject neglect the issue of the relevance of such logics in relation with the intended meaning of the third truth value. Here, we focus on the case where the third truth-value means unknown, as suggested...

Abstract In 2016, Béziau introduces a restricted notion of paraconsistency, the so-called genuine paraconsistency. A logic is paraconsistent if it rejects laws $\varphi ,\neg \varphi \vdash \psi $ and $\vdash \neg (\varphi \land )$. that paper, author analyzes, among three-valued logics, which them satisfy this property. If we consider multiple-conclusion consequence relations, dual properties ...

A Hennessy-Milner property, relating modal equivalence and bisimulations, is defined for many-valued modal logics that combine a local semantics based on a complete MTL-chain (a linearly ordered commutative integral residuated lattice) with crisp Kripke frames. A necessary and sufficient algebraic condition is then provided for the class of image-finite models of these logics to admit the Henne...

We consider propositional logic. Three-valued logics are old: the first one is Lukasiewicz three valued logic from 1920 [8]. Gödel in [5] from 1932 studied a hierarchy of finite-valued logics, containing Gödel three-valued logic. Our main interest pays to Kleene three-valued logic [6]. Other threevalued logics will not be considered here. Let us agree that the three truth values are 0, 1 2 , 1 ...