In this paper we present a sound and complete axiom system for a probabilistic process algebra with recursion. Soundness and completeness of the axiomatization is given with respect to the testing semantics deened in 19].

We develop a sound and strongly complete axiomatic system for probabilistic logic in which we can model nonmonotonic (or default) reasoning. We discuss the connection between previously developed logics and the two sublogics of the logic presented here.

We extend Milner's SCCS to obtain a calculus, PCCS, for reasoning about communicating probabilistic processes. In particular, the nondeterministic process summation operator of SCCS is replaced with a probabilistic one, in which the probability of behaving like a particular summand is given explicitly. The operational semantics for PCCS is based on the notion of probabilistic derivation, and is...

Abrial’s Generalised Substitution Language (GSL) [4] can be modified to operate on arithmetic expressions, rather than Boolean predicates, which allows it to be applied to probabilistic programs [13]. We add a new operator p⊕ to GSL, for probabilistic choice, and we get the probabilistic Generalised Substitution Language (pGSL): a smooth extension of GSL that includes random algorithms within i...

Probabilistic model checking is a powerful formal verification method that can ensure the correctness of real-life systems that exhibit stochastic behaviour. The work presented in this thesis aims to solve the scalability challenge of probabilistic model checking, by developing, for the first time, fully-automated compositional verification techniques for probabilistic systems. The contribution...

By using the probabilistic method, we show that the maximum number of directed Hamiltonian paths in a complete directed graph with n vertices is at least (e− o(1)) n! 2n−1 .

assessment of the correlation between rock brittleness and rock fracture toughness has been the subject of extensive research works in the recent years. unfortunately, the brittleness measurement methods have not yet been standardized, and rock fracture toughness cannot be estimated satisfactorily by the proposed indices. in the present study, statistical analyses are performed on some data col...

one of the main distinctions between geomaterials and other engineering materials is the spatial variation of their properties in different directions. this characteristic of geomaterials -so called heterogeneity- is studied herewith. several spatial distributions are introduced to describe probabilistic variation of geotechnical properties of soils. among all, the absolute normal distribution ...

the purpose of this study is to compare the results of different probabilistic methods such as the perturbation method, stochastic finite element method (sfem) and monte carlo method. these methods were used to study the convergence of direct approach for slope stability analysis and are developed for a linear soil behavior. in this study, two dimensional random fields are used and both the fir...

This paper studies connections between two alternatives to the standard probability calculus for representing and reasoning about uncertainty: imprecise comparative probability. The goal is identify complete logics uncertainty in a probabilistic language whose semantics given terms of Comparative operators are interpreted as quantifying over set measures. Modal dynamic added epistemic possibili...