We consider the modal-calculus due to Kozen, which is a nitary modal logic with least and greatest xed points of monotone operators. We extend the existing duality between the category of modal algebras with homomorphisms and the category of descriptive modal frames with contractions to the case of having xed point operators. As a corollary, we obtain a completeness result for Kozen's original ...

Modal mu-calculus [5] is a logical framework combining simple modalities with fixed point operators, enriching the expressivity of modal logic so as to deal with infinite processes like recursion. It has a simple syntax, an easily given semantics, and is decidable. Many expressive modal and temporal logics such as PDL, CTL and CTL∗ can be seen as fragments of the modal mu-calculus. Sahlqvist-st...

In this paper, a computationally simple approach for damage localization and quantification in beam-like structures is proposed. This method is based on using modal flexibility curvature (MFC) and particle swarm optimization (PSO) algorithm. Analytical studies in the literature have shown that changes in the modal flexibility curvature can be considered as a sensitive and suitable criterion for...

We define an interpretation of modal languages with polyadic operators in modal languages that use monadic operators (diamonds) only. We also define a simulation operator which associates a logic Λ in the diamond language with each logic Λ in the language with polyadic modal connectives. We prove that this simulation operator transfers several useful properties of modal logics, such as finite/r...

Taking Löb’s Axiom in modal provability logic as a running thread, we discuss some general methods for extending modal frame correspondences, mainly by adding fixed-point operators to modal languages as well as their correspondence languages. Our suggestions are backed up by some new results — while we also refer to relevant work by earlier authors. But our main aim is advertizing the perspecti...

In this paper we describe an algorithmic framework for a multi-modal logic arising from the combination of the system of modal (epistemic) logic devised by Meyer and van der Hoek for dealing with nonmonotonic reasoning with a deontic logic of the Jones and Pörn-type. The idea behind this (somewhat eclectic) formal set-up is to have a modal framework expressive enough to model certain kinds of d...

Modal and modal-like formalisms such as temporal or description logics go beyond propositional logic by introducing operators that allow for a guarded form of quantification over states or paths of transition systems. Thus, they are more expressive than propositional logic, yet computationally better behaved than first-order logic. We propose constraint-based methods to model and solve modal sa...

The SCAN algorithm has been proposed for second order quanti er elimination. In particular it can be applied to nd correspondence axioms for systems of modal logic. Up to now, what has been studied are systems with unary modal operators. In this paper we study how SCAN can be applied to various systems of conditional logic, which are logical systems with binary modal operators.

Taking Löb's Axiom in modal provability logic as a running thread, we discuss some general methods for extending modal frame correspondences, mainly by adding fixedpoint operators to modal languages as well as their correspondence languages. Our suggestions are backed up by some new results – while we also refer to relevant work by earlier authors . But our main aim is advertizing the perspecti...

A bilattice is a set equipped with two partial orders and a negation operation that inverts one of them while leaving the other unchanged; it has been suggested that the truth values used by inference systems should be chosen from such a structure instead of the two-point set {t, f}. Given such a choice, we redefine a modal operator to be a function on the bilattice selected, and show that this...