A notation for probabilities is proposed that differs from the traditional, conventional notation by making explicit the domains and bound variables involved. The notation borrows from the Z notation, and lends itself well to calculational manipulations, with a smooth transition back and forth to set and predicate notation.

Away is found to add axioms to sequent calculi that maintains the eliminability of cut, through the representation of axioms as rules of inference of a suitable form. By this method, the structural analysis of proofs is extended from pure logic to free-variable theories, covering all classical theories, and a wide class of constructive theories. All results are proved for systems in which also ...

In this paper we propose higher-order rewrite systems without bound variables. In order to prove their connuence under the assumption of orthogonality, we study a simple proof method which employs a characterization of the diamond property of a parallel reduction. By an application of the proof method, we obtain a new connuence result for orthogonal higher-order conditional rewrite systems.

Every theory we will consider will be in a language that has a name ṅ for each n ∈ ω. For example, the name for 2 ∈ ω in the language LΩ of arithmetic is the term “1 + 1”. The results stated will only apply to countable languages. This requirement is implicit in the hypothesis of the existence of an enumeration of all formulas with one free variable, for example. We also assume that formulas an...

In this paper, we introduce a new fragment of the rst-order temporal language, called the monodic fragment, in which all formulas beginning with a temporal operator (Since or Until) have at most one free variable. We show that the satissability problem for monodic formulas in various linear time structures can be reduced to the satissability problem for a certain fragment of classical rst-order...

Assume we are given (finitely many) mutually independent variables and (finitely many) “undesirable” events each depending on a subset of the variables of at most k elements, known as the scope of the event. Assume that the probability of an individual variable belonging to the scope of an occurring event is bounded by q. We prove that if ekq ≤ 1 then there exists at least one assignment to the...

Abstracr-Test data generation in program testing is the process of identifying a set of test data which satisfies given testing criterion. Most of the existing test data generators 161, [It], [lo], [16], [30] use symbolic evaluation to derive test data. However, in practical programs this technique frequently requires complex algebraic manipulations, especially in the presence of arrays. In thi...

A modified generalised directional distance function data envelopment analysis model is introduced into the smoothed bootstrap context. The new handles asymmetrically desirable and undesirable outputs deals with positive negative values, while bias-corrected estimators are independent of length direction vector. reason for development this efficiency assessment estimation degree operating gains...

Spearman’s rank correlation coefficient is a nonparametric (distribution-free) rank statistic proposed by Charles Spearman as a measure of the strength of an association between two variables. It is a measure of a monotone association that is used when the distribution of data makes Pearson’s correlation coefficient undesirable or misleading. Spearman’s coefficient is not a measure of the linea...

Spearman’s rank correlation coefficient (denoted here by rs) is a nonparametric (distribution-free) rank statistic proposed by Charles Spearman as a measure of the strength of the associations between two variables. It is a measure of a monotone association that is used when the distribution of the data makes Pearson’s correlation coefficient undesirable or misleading. Spearman’s coefficient is...