Abstract: Functions defining a distance and a distinguish degree between objects described by predicate formulas are introduced. It is proved that the introduced function of distance satisfies all properties of a distance. The function of objects distinguish degree adequately reflects similarity

of various entities. Included are nonmonotonic treatments of is-a hierarchies, the unique names hypothesis, and the frame problem. The new circumscription may be called formula circumscription to distinguish it from the previously defined domain circumscription and predicate circumscription. A still more

It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology. Here “reduced ” means, roughly speaking, that the first problem can be solved

verification for the formulas of

at most k . 'Invariance for k--partial isomorphism' means having the same truth value at tuples of objects in any two models that are connected by a partial isomorphism in such a set. The precise sense of this is spelt out in the following proof. 21 Proof (Outline.) k-variable formulas

/definitely/currently interpretation such a predicate becomes well-defined, without requiring it to be recast using temporal formulas. Further, our algorithms may be more efficient than techniques that use a notion of explicit time or process histories. Section 1 specifies the protocols and Section 2 gives an outline of

This reports some experiences with a recently-implemented prototype system for verification using predicate abstraction, based on the method of Graf and Saidi [9]. Systems are described using a language of iterated guarded commands, called MurOE \Gamma\Gamma (since it is a simplified version

by formulas in ¨L³, the subset of First Order Predicate Calculus with monadic and dyadic predicates which allows only three variable symbols. In order to handle “number bounds”, we allow numeric quantifiers, and for transitive closure of roles we use infinitary disjunction. Using previous results

variables, where the system state includes mutable functions and predicates. Such a model can describe systems containing arbitrarily large memories, buffers, and arrays of identical processes. We describe a form of predicate abstraction that constructs a formula over a set of universally quantified

is the semantic type of VPs? One answer is that VPs are 1-place predicates. An alternative answer is that VPs are formulas.1 For example, the LF-representation for John left on the "predicates " hypothesis may be (1). (1) [S John [VP left]] On the "formulas " hypothesis, the same sentence has