We study the problem of embedding Halpern and Moses’s modal logic of minimal knowledge states into two families of modal formalism for nonmonotonic reasoning, McDermott and Doyle’s nonmonotonic modal logics and ground nonmonotonic modal logics. First, we prove that Halpern and Moses’s logic can be embedded into all ground logics; moreover, the translation employed allows for establishing a lowe...

The aim of this paper is to study the n-variable fragment of rst order logic from a modal perspective. We deene a modal formalism called cylindric mirror modal logic, and show how it is a modal version of rst order logic with substitution. In this approach, we can deene a semantics for the language which is closely related to algebraic logic, as we nd Polyadic Equality Algebras as the modal or ...

CoLoSS, the Coalgebraic Logic Satisfiability Solver, decides satisfiability of modal formulas in a generic and compositional way. It implements a uniform polynomial space algorithm to decide satisfiability for modal logics that are amenable to coalgebraic semantics. This includes e.g. the logics K, KD, Pauly’s coalition logic, graded modal logic, and probabilistic modal logic. Logics are easily...

This paper introduces modal independence logic MIL, a modal logic that can explicitly talk about independence among propositional variables. Formulas of MIL are not evaluated in worlds but in sets of worlds, so called teams. In this vein, MIL can be seen as a variant of Väänänen’s modal dependence logic MDL. We show that MIL embeds MDL and is strictly more expressive. However, on singleton team...

The aim of this paper is to study the n variable fragment of rst order logic from a modal perspective We de ne a modal formalism called cylindric mirror modal logic and show how it is a modal version of rst order logic with substitution In this approach we can de ne a semantics for the language which is closely related to algebraic logic as we nd Polyadic Equality Algebras as the modal or compl...

In [1] the authors considered finitely-valued modal logics with Kripke style semantics where both propositions and the accessibility relation are valued over a finite residuated lattice. Unfortunately, the necessity operator does not satisfy in general the normality axiom (K). In this paper we focus on the case of finite chains, and we consider a different approach based on introducing a multim...

Godel's translation of intuitionistic formulas into modal ones provides the well-known embedding of intermediate logics into extensions of Lewis' system S4, which re ects and sometimes preserves such properties as decidability, Kripke completeness, the nite model property. In this paper we establish a similar relationship between intuitionistic modal logics and classical bimodal logics. We als...

In this paper, we generalize the set-theoretic translation method for polymodal logic introduced in 11] to extended modal logics. Instead of devising an ad-hoc translation for each logic, deening a new set-theoretic function symbol for each new modal operator, we develop a general framework within which a number of extended modal logics can be dealt with. More precisely, we extend the basic set...

In this paper we present completeness results of several fuzzy logics trying to capture different notions of necessity (in the sense of Possibility theory) for Gödel logic formulas. In a first attempt, based on different characterizations of necessity measures on fuzzy sets, a group of logics, with Kripke style semantics, are built over a restricted language, indeed a two level language compose...

We propose a semantic representation of the standard quantum logic QL within a classical, normal modal logic, and this via a lattice-embedding of orthomodular lattices into Boolean algebras with one modal operator. Thus our classical logic is a completion of the quantum logic QL. In other words, we refute Birkhoff and von Neumann’s classic thesis that the logic (the formal character) of Quantum...