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...

Correspondence to: E Herrett [email protected] Extra material supplied by the author (see http://www.bmj.com/content/346/bmj.f2350?tab=related#webextra) Supplementary figures 1-4 Supplementary table 1 Supplementary table 2 Supplementary table 3 Supplementary table 4 Supplementary table 5 Supplementary table 6 Supplementary table 7 Supplementary table 8 Supplementary table 9 Supplementar...

This paper investigates the relation between wood dust exposure in the furniture industry and occupational hygiene variables. During the winter 1997-98 54 factories were visited and 2362 personal, passive inhalable dust samples were obtained; the geometric mean was 0.95 mg/m(3) and the geometric standard deviation was 2.08. In a first measuring round 1685 dust concentrations were obtained. For ...

In order to assist the performance evaluation of complex stochastic models, automatic program tools were developed since a long time. Stochastic Petri Nets (SPN) are applied as an effective model description language supported by several analytical and simulation tools. The analytical description and the numerical analysis of non-Markovian stochastic Petri Net models gained attention recently. ...

It follows that the E-step splits into an E-W step and an E-Z step. The subsequent M-step can also be divided into two steps referred to as the M-GMM step and the M-mapping step. In what follows details are given for the E-W step and the M-mapping step as the E-Z and M-GMM steps are straightforward as explained in the main paper (equations (27) to (30. For the sake of readability, the current i...