This paper presents a general method for proving termination of tableaux-based procedures for modal-type logics and related firstorder fragments. The method is based on connections between filtration arguments and a general blocking technique. The method provides a general framework for developing tableau-based decision procedures for a large class of logics. In particular, the method can be ap...

We investigate the higher-order modal logic SωI , which is a variant of the system Sω presented in our previous work. A semantics for that system, founded on the theory of quasi sets, is outlined. We show how such a semantics, motivated by the very intuitive base of Schrödinger logics, provides an alternative way to formalize some intensional concepts and features which have been used in recent...

We present a semantic tableaux calculus for propositional nonmonotonic modal logics, based on possible-worlds characterisations for nonmonotonic modal logics. This method is parametric with respect to both the modal logic and the preference semantics, since it handles in a uniform way the entailment problem for a wide class of nonmonotonic modal logics: McDermott and Doyle's logics and ground l...

Justification logics were introduced by Artemov in 1995 to provide intuitionistic logic with a classical provability semantics, a problem originally posed by Gödel. Justification logics are refinements of modal logics and formally connected to them by so-called realization theorems. A constructive proof of a realization theorem typically relies on a cut-free sequent-style proof system for the c...

Combining non-classical or`sub-classical' logics is not easy, but it is very interesting. In this paper, we combine nonclassical logics of negation and possibility in the presence of conjunction and disjunction, and then we combine the resulting systems with intuitionistic logic. We will nd that Kracht's results on the undecidability o f classical modal logics generalise to a non-classical sett...

Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit counterparts to modal logics. The behavior and interaction of agents in distributed system is often modeled using logics of knowledge and time. In this paper, we sketc...

We investigate the topological interpretation of modal logic in modern terms, using a new notion of bisimulation. We look at modal logics with interesting topological content, presenting, among others, a new proof of McKinsey and Tarski’s theorem on completeness of S4 with respect to the real line, and a completeness proof for the logic of finite unions of convex sets of reals. We conclude with...