Recent advances in Multiagent Systems (MAS) and Epistemic Logic within Distributed Systems Theory, have used various combinatorial structures that model both the geometry of the systems and the Kripke model structure of models for the logic. Examining one of the simpler versions of these models, interpreted systems, and the related Kripke semantics of the logic S5n (an epistemic logic with n-ag...

This thesis presents efficient parallel algorithms for checking temporal logic formulas over finite paths and trees. We show that LTL path checking is in AC(logDCFL) and CTL tree checking is in AC(logDCFL). For LTL with pasttime and bounded modalities, which is an exponentially more succinct logic, we show that the path checking problem remains in AC(logDCFL). Our results provide a foundation f...

Building on the fact that descriptive frames are coalgebras for the Vietoris functor on the category of Stone spaces, we introduce and study the concept of a Vietoris bisimulation between two descriptive modal models, together with the associated notion of bisimilarity. We prove that our notion of bisimilarity, which is defined in terms of relation lifting, coincides with Kripke bisimilarity (w...

Abstract We study a generalization of the notion conservativity spectrum an arithmetical theory to language with transfinitely many truth definitions. establish natural correspondence spectra and points special Kripke model introduced studied by D. Fernández–Duque J. Joosten. For iterated reflection principles over theories definitions we also conservation results analogous well-known Schmerl f...

In this paper we consider the problem of computing and representing the bisimulation on a given Kripke structure. Such a problem, central in Model Checking, has been tackled by many authors and various solutions have been given. In particular, the algorithm proposed by Kanellakis and Smolka [7] is used in many model checkers with explicit-state representation, while the algorithm proposed by Bo...

The Brouwer-Heyting-Kolmogorov interpretation of intuition-istic logic suggests that p q can be interpreted as a computation that given a proof of p constructs a proof of q. Dually, we show that every nite canonical model of q contains a nite canonical model of p. If q and p are interderivable, their canonical models contain each other. Using this insight, we are able to characterize validity i...

In this course, we have seen several modal logics and proof calculi to justify the truth / validity of formulas. But natural deduction, Hilbert-style calculi, tableaux, sequent calculi and the like are not the only way to establish truth. For a particular Kripke structure at hand, a systematic exploration of the state space can be used to establish if a formula of modal logic is true or false i...