We present a purely syntactical deenition of E.W. Dijkstra's predicate transformer wp for nondeterministic while-programs in innnitary logic. Then we show that it is sound wrt. a deenition of weakest preconditions given in terms of denotational semantics.

Abstract We present a semantic framework for the deductive verification of hybrid systems with Isabelle/HOL. It supports reasoning about temporal evolutions programs in style differential dynamic logic modelled by flows or invariant sets vector fields. introduce foundations this and summarise their Isabelle formalisation as well resulting components. A series simple examples shows our approach ...

Condition monitoring of electrical power equipment has attracted considerable attention for many years. The aim of this paper is to use Labview with Fuzzy Logic controller to build a simulation system to diagnose transformer faults and monitor its condition. The front panel of the system was designed using LabVIEW to enable computer to act as customer-designed instrument. The dissolved gas-in-o...

For two parallel languages with recursion a compositional weakest precondition semantics is given using two new metric resumption domains. The underlying domains are characterized by domain equations involving functors that deliveròbservable' and`safety' predicate transformers. Further a reenement relation is deened for this domains and illustrated by rules dealing with concurrent composition. ...

We deene a predicate transformer, in terms of which nite disjunctions of leads-to properties can be rewritten as single leads-to properties. Although disjunctions of leads-to properties do not typically arise naturally in progress speciications, an example shows how they may be introduced through the use of nested implications of leads-to properties; such implications allow subtle dependencies ...

Action systems were originally proposed for the design of parallel and distributed systems in a stepwise manner. Later the formalism has been successfully applied to the design of control systems. When designing control systems very often it is necessary to reason about, e.g. the probabilistic reliability of a controller or some other types of prob-abilistic phenomena. Within action systems for...

We contrast the use of weakest preconditions for the correct construction of procedures with the cumulative subgoal fulfillment (CSF) approach. An example of Cohen and Monin is used for this purpose. The CSF construction process is demonstrated.

We study a number of conditions on the Hilbert function of a level artinian algebra which imply the Weak Lefschetz Property (WLP). Possibly the most important open case is whether a codimension 3 SI-sequence forces the WLP for level algebras. In other words, does every codimension 3 Gorenstein algebra have the WLP? We give some new partial answers to this old question: we prove an affirmative a...

The aim of the present paper is to define and study (IC)$LM$-fuzzytopological spaces, a generalization of (weakly) induced $LM$-fuzzytopological spaces. We discuss the basic properties of(IC)$LM$-fuzzy topological spaces, and introduce the notions ofinterior (IC)-fication and exterior (IC)-fication of $LM$-fuzzytopologies and prove that {bf ICLM-FTop} (the category of(IC)$LM$-fuzzy topological ...

The behavior of a program can be modeled by describing how it transforms input states to output states, the state transformer semantics. Alternatively, for verification purposes one is interested in a ’predicate transformer semantics’ which, for every condition on the output, yields the weakest precondition on the input that guarantees the desired property for the output. In the presence of com...