and validation systems. Usually, we distinguish three families of tools: model checkers (SMV [6], SPIN [11]) to build a finite model and check its temporal properties; automatic proof tools (Mona [10] for the WSnS logic, its extension to structured types Lisa [2]), and proof assistants (Coq [3], HOL [8] and PVS

of temporal logics based on experiments, and we present model-checking algorithms for the verif...

Abstract Basic ideas of rough set theory were proposed by Zdzis law Pawlak [85, 86] in the early 1980’s. In the ensuing years, we have witnessed a systematic, world–wide growth of interest in rough sets and their applications. The main goal of rough set analysis is induction of approximations of con-cepts. This main goal is motivated by the basic fact, constituting also the main problem of KDD, that languages we may choose for knowledge description are incomplete. A fortiori, we have to describe concepts of interest (features, proper-ties, relations etc.) not completely but by means of their reflections (i.e. approx-imations) in the chosen language. The most important issues in this induction process are: – construction of relevant primitive concepts from which approximations of more complex concepts are assembled, – measures of inclusion and similarity (closeness) on concepts, – construction of operations producing complex concepts from the primitive ones.

. It supports a wide spectrum of formal methods, including: executable specification; symbolic simulation; breadth-first search for failures of safety properties in infinite-state systems; and linear temporal logic model checking of time-bounded temporal logic formulas. These methods complement those offered

that achieve their QoS requirements through dynamically adapting to changes in the system state, environment, and workload. QoSMOS service-based systems translate high-level QoS requirements specified by their administrators into probabilistic temporal logic formulae, which are then formally and automatically

, of preconditions and ramifications of actions, the modelling of system faults, and most of all, the representation of uncertainty of actions. As the underlying language, the Open Logic Programming formalism, an extension of Logic Programming, is used. The experiment shows that Event Calculus is a promising

Abstract. This paper discusses experiments with a “model-based ” approach for developing verified distributed systems in which program development is carried out by stepwise refinement: we encode, specifications and algorithm archetypes in the PVS theorem prover, carry out stepwise refinement

. It supports a wide spectrum of formal methods, including: executable specification; symbolic simulation; breadth-first search for failures of safety properties in infinite-state systems; and linear temporal logic model checking of time-bounded temporal logic formulas. These methods complement those oered

. In particular, the Randall-Sundrum model is well-known for achieving an amelioration of the hierarchy problem. However, the basic model relies on Minkowski branes and is subject to solar system constraints in the absence of a radion stabilization mechanism. We present a method by which a four-dimensional low

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