Rewrite theories and their associated Kripke structures constitute a flexible and executable framework in which a wide range of systems can be studied. We present a general notion of simulation between Kripke structures, study its categorical aspects, and propose rewriting logic as a framework in which these simulations can be represented. Several representability results showing that rewriting...

this paper presents a mathematical model for a flow shop scheduling problem consisting of m machine and n jobs with fuzzy processing times that can be estimated as independent stochastic or fuzzy numbers. in the traditional flow shop scheduling problem, the typical objective is to minimize the makespan). however,, two significant criteria for each schedule in stochastic models are: expectable m...

The usual epistemic S5 model for multi-agent systems is a Kripke graph, whose edges are labeled with the agents that do not distinguish between two states. We propose to uncover the higher dimensional information implicit in the Kripke graph, by using as a model its dual, a chromatic simplicial complex. For each state of the Kripke model there is a facet in the complex, with one vertex per agen...

Normal forms for propositional modal logics are used to establish the Kripke completeness, the finite model property, and the decidability for modal logics KB and KTB.

We analyze the asymptotic conditional validity of modal formulas, i.e., the probability that a formula ψ is valid in the finite Kripke structures in which a given modal formula φ is valid, when the size of these Kripke structures grows to infinity. We characterize the formulas ψ that are almost surely valid (i.e., with probability 1) in case φ is a flat, S5consistent formula, and show that thes...

Every group is isomorphic to the automorphism group of a Kripke structure with Boolean part equal to a power set Boolean algebra. More generally, we prove that the category of Kripke structures with Boolean part equal to a power set Boolean algebra and morphisms with complete Boolean part is alg-universal, which means that it contains any category of universal algebras as a full subcategory.

The completeness of the modal logic S4 for all topological spaces as well as for the real line R, the n-dimensional Euclidean space R and the segment (0, 1) etc. (with 2 interpreted as interior) was proved by McKinsey and Tarski in 1944. Several simplified proofs contain gaps. A new proof presented here combines the ideas published later by G. Mints and M. Aiello, J. van Benthem, G. Bezhanishvi...

We survey notions of bisimulation and of bisimilar coverings both in the world of graph-like structures (Kripke structures, transition systems) and in the world of hypergraph-like general relational structures. The provision of finite analogues for full infinite tree-like unfoldings, in particular, raises interesting combinatorial challenges and is the key to a number of interesting model-theor...

We present an investigation of duality in the traditional logical manner. We extend Nelson's symmetrization of intuitionistic logic, constructible falsity, to a self-dual logic; constructible duality. We develop a self-dual model by considering an interval of worlds in an intuitionistic Kripke model. The duality arises through how we judge truth and falsity. Truth is judged forward in the Kripk...

This paper describes a framework, based on Abstract Interpretation, for creating abstractions for model-checking. Specifically, we study how to abstract models of calculus and systematically derive abstractions that are constructive, sound, and precise, and apply them to abstracting Kripke structures. The overall approach is based on the use of bilattices to represent partial and inconsistent i...