Interpretability logic is a modal description of the interpretability predicate. The modal system IL is an extension of the provability logic GL (Gödel–Löb). Bisimulation quotients and largest bisimulations have been well studied for Kripke models. We examine interpretability logic and consider how these results extend to Veltman models. REPORTS ON MATHEMATICAL LOGIC 40 (2006), 59–73 Domagoj VR...

We introduce a family of modal expansions of Belnap-Dunn four-valued logic and related systems, and interpret them in many-valued Kripke structures. Using algebraic logic techniques and topological duality for modal algebras, and generalizing the so-called twist-structure representation, we axiomatize by means of Hilbert-style calculi the least modal logic over the four-element Belnap lattice a...

There are two main objectives of this paper. The first is to present a statistical framework for models with context specific indepen­ dence structures, i.e. conditional independen­ cies holding only for specific values of the con­ ditioning variables. This framework is consti­ tuted by the class of split models. Split mod­ els are an extension of graphical models for contingency tables and all...

The subject of this article is Modal-Epistemic Arithmetic, a theory introduced by Horsten to interpret Epistemic Arithmetic, which in turn was introduced by Shapiro to interpret Heyting Arithmetic. I will show how to interpret Modal-Epistemic Arithmetic in Epistemic Arithmetic and I will show how to get rid of a particular Platonist assumption. Then I will discuss models for Modal-Epistemic Ari...

We present a new kind of simulation with the aim of using it as minimality criterion for models of modal logics. We discuss such minimality criterion by comparing it with minimal modal Herbrand models. Even though our final goal is the automated generation of minimal models through a tableau-based method, this paper is on a theoretical level and does not aim to propose algorithms on how to gene...

Positive Modal Logic is the restriction of the modal local consequence relation defined by the class of all Kripke models to the propositional negation-free modal language. The class of positive modal algebras is the one canonically associated with PML according to the theory of Abstract Algebraic Logic. In [4], a Priestley-style duality is established between the category of positive modal alg...

The two-dimensional modal logic of Davies and Humberstone [3] is an important aid to our understanding the relationship between actuality, necessity and a priori knowability. I show how a cut-free hypersequent calculus for 2d modal logic not only captures the logic precisely, but may be used to address issues in the epistemology and metaphysics of our modal concepts. I will explain how use of o...