In this paper, we describe some practical applications of probabilistic model checking, a technique for the formal analysis of systems which exhibit stochastic behaviour. We give an overview of a selection of case studies carried out using the probabilistic model checking tool PRISM, demonstrating the wide range of application domains to which these methods are applicable. We also illustrate se...

Probabilistic transition system specifications (PTSS) provide structural operational semantics for reactive probabilistic labeled transition systems. Bisimulation equivalences and bisimulation metrics are fundamental notions to describe behavioral relations and distances of states, respectively. We provide a method to generate from a PTSS a sound and ground-complete equational axiomatization fo...

This paper proposes two probabilistic extensions of variants of the OWL Lite description language, which are essential for advanced applications like information retrieval. The first step follows the axiomatic approach of combining description logics and Horn clauses: Subsets of OWL Lite are mapped in a sound and complete way onto Horn predicate logics (Datalog variants). Compared to earlier ap...

We consider sequential and concurrent probabilistic processes and propose a general notion of fairness with respect to probabilistic choice, which allows to express various notions of fairness such as process fairness and event fairness. We show the soundness of proving the validity of qualitative properties of probabilistic processes under fairness constraints in the sense that whenever all fa...

This article presents a probabilistic logic whose sentences can be interpreted as asserting the acceptability of gambles described in terms of an underlying logic. This probabilistic logic has a concrete syntax and a complete inference procedure, and it handles conditional as well as unconditional probabilities. It synthesizes Nilsson’s probabilistic logic and Frisch and Haddawy’s anytime infer...

We consider sequential and concurrent probabilistic processes and propose a general notion of fairness with respect to probabilistic choice, which allows to express various notions of fairness such as process fairness and event fairness. We show the soundness of proving the validity of qualitative properties of probabilistic processes under fairness constraints in the sense that whenever all fa...

Probabilistic reasoning under the so-called principle of maximum entropy is a viable and convenient alternative to Bayesian networks, relieving the user from providing complete (local) probabilistic information and observing rigorous conditional independence assumptions. In this paper, we present a novel approach to performing computational MaxEnt reasoning that makes use of symbolic computatio...

We formalize a mathematical approach to probabilistic logic for zero-order logic and derive new inequalities that are necessary and sufficient for consistent probability assignments to propositions. We prove that a complete theory of probabilistic logic requires the a priori assignment of probabilities for a system with k basic propositions. We also show that a proposal due to Cheeseman, namely...

It is well-known that constructing models of higher-order probabilistic programming languages is challenging. We show how to construct step-indexed logical relations for a probabilistic extension of a higher-order programming language with impredicative polymorphism and recursive types. We show that the resulting logical relation is sound and complete with respect to the contextual preorder and...

Belief maintenance systems are natural extensions of truth maintenance systems that use probabilities rather than boolean truth-values. This paper introduces a general method for belief maintenance, based on (the propositional fragment of) probabilistic logic, that extends the Boolean Constraint Propagation method used by the logic-based truth maintenance systems. From the concept of probabilis...