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...

We propose a model for modular synchronous systems with combinational dependencies and define consistency using this model. We then show how to derive this model from a modular specification where individual modules are specified as Kripke Structures and give an algorithm to check the system for consistency. We have implemented this algorithm symbolically using BDDs in a tool, SpecCheck. We hav...

This paper presents a novel theoretical framework for the state space reduction of Kripke structures. We define two equivalence relations, Kripke minimization equivalence (KME) and weak Kripke minimization equivalence (WKME). We define the quotient system under these relations and show that these relations are strictly coarser than strong (bi)simulation and divergence-sensitive stutter (bi)simu...

In this paper is presented an update of the model checker CTL. The minimal modifications which appear represent the fundamental concept for model the dynamic system. In the paper used five primitive operations discompose from the operation of a CTL update used already by [1] which are presented their approach of knowledge update the structures of single agent S5 Kripke. Then is willed defined t...

In lecture 7, we have seen how axiomatics and semantics of modal logic fit together in soundness proofs and correspondence proofs. We have seen several examples of classes of Kripke frames that are characterized by formulas of propositional modal logic. These were several special cases. But we are looking for a general correspondence result. Can we find a full correspondence result? For any for...

Temporal logic query checking was first introduced by W. Chan in order to speed up design understanding by discovering properties not known a priori. A query is a temporal logic formula containing a special symbol ?1, known as a placeholder. Given a Kripke structure and a propositional formula ’, we say that ’ satisfies the query if replacing the placeholder by ’ results in a temporal logic for...