The temporal property`to-always' has been proposed for specifying progress properties of concurrent programs. Although thèto-always' properties are a subset of thèleads-to' properties for a given program, `to-always' has more convenient proof rules and in some cases more accurately describes the desired system behavior. In this paper, we give a predicate transformer wta, derive some of its prop...

We study the recognition problem in the metaprogramming of finite normal predicate logic programs. That is, let L be a computable first order predicate language with infinitely many constant symbols and infinitely many n-ary predicate symbols and n-ary function symbols for all n ≥ 1. Then we can effectively list all the finite normal predicate logic programs Q0, Q1, . . . over L. Given some pro...

Simulation rules provide a simple, sound and complete technique for proving that one data type reenes another. This paper expresses the dependence of the sound-ness and completeness on the programming language by showing how sound and complete simulation rules for a given language are derived from those for its sublanguages. The dependence of the completeness on the semantic model is expressed ...

In this paper we revisit the well-known technique of predicate abstraction to characterise performance attributes of system models incorporating probability. We recast the theory using expectation transformers [8], and identify transformer properties which correspond to abstractions that yield nevertheless exact bound on the performance of infinite state probabilistic systems. In addition, we e...

Modal Kleene algebras are Kleene algebras with forward and backward modal operators, defined via domain and codomain operations. They provide a concise and convenient algebraic framework that subsumes various popular calculi and allows treating quite a number of areas. We survey the basic theory and some prominent applications. These include, on the system semantics side, wlp and wp calculus, P...

The behaviour of logic programs (with various built-in's) is described in terms of sets of substitutions associated with the control points of the program. These sets are deened by means of an operational semantics O, based on a description of uniication as predicate transformer. It is shown that O subsumes the semantics of logic programs consisting of the set of computed substitutions obtained...

We show that the set of valid formulas in Lukasiewicz predicate logic is a complete Π 2 set. We also show that the classically valid formulas are exactly those formulas in the classical language whose fuzzy value is 1/2. Lukasiewicz’ infinite valued logic can be seen as a particular “implementation” of fuzzy logic. The set of possible “truth values” (or, in another interpretation, degrees of ce...

The paper deals with fuzzy Horn logic (FHL) which is a fragment of predicate fuzzy logic with evaluated syntax. Formulas of FHL are of the form of simple implications between identities. We show that one can have Pavelka-style completeness of FHL w. r. t. semantics over the unit interval [0, 1] with (residuated lattices given by) left-continuous t-norm and a residuated implication, provided tha...

Recent development of mathematical fuzzy logic is brieey surveyed. The set of all formulas of predicate logic that are tautologies with respect to all continuous t-norms is shown to be heavily non-recursive ((2-hard).

This paper presents the application of the fuzzy-neuro method toinvestigate transformer inrush current. Recently, the frequency environment ofpower systems has been made more complicated and the magnitude of the secondharmonic in inrush current has been decreased because of the improvement of caststeel. Therefore, traditional approaches will likely mal-operate in the case ofmagnetizing inrush w...