the fuzzy linear regression model with fuzzy input-output data andcrisp coefficients is studied in this paper. a linear programmingmodel based on goal programming is proposed to calculate theregression coefficients. in contrast with most of the previous works, theproposed model takes into account the centers of fuzzy data as animportant feature as well as their spreads in the procedure ofconstr...

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...

In the elementary case of finitely many events, we generalise to Gödel (propositional infinite-valued) logic — one of the fundamental fuzzy logics in the sense of Hájek — the classical correspondence between partitions, quotient measure spaces, and push-forward measures. To achieve this end, appropriate Gödelian analogues of the Boolean notions of probability assignment and partition are needed...