Probabilistic abduction extends conventional symbolic abductive reasoning with Bayesian inference methods. This allows for the uncertainty underlying implications to be expressed with probabilities as well as assumptions, thus complementing the symbolic approach in situations where the use of a complete list of assumptions underlying inferences is not practical. However, probabilistic abduction...

ion refinement techniques in probabilistic model checking are prominent approaches to the verification of very large or infinite-state probabilistic concurrent systems. At the core of the refinement step lies the implicit or explicit analysis of a counterexample. This paper proposes an abstraction refinement approach for the probabilistic computation tree logic (PCTL), which is based on increme...

Simulations and bisimulations are known to be useful for abstracting and comparing formal systems, and they have recently been introduced into fuzzy systems. In this study, we provide sound and complete logical characterizations for simulation and bisimulation, which are defined over fuzzy labeled transition systems via two variants of the Hennessy-Milner Logic. The logic for characterizing fuz...

We survey various notions of probabilistic automata and probabilistic bisimulation, accumulating in an expressiveness hierarchy of probabilistic system types. The aim of this paper is twofold: On the one hand it provides an overview of existing types of probabilistic systems and, on the other hand, it explains the relationship between these models. We overview probabilistic systems with discret...

The computational delay of a circuit can be described by the natural concept of time Jakoby et al. STOC94]. We show that for a given input x and circuit C the computation of timeC(x) is P-complete. Moreover, we show that it is NP-complete to decide whether there exists an input x such that timeC(x) t for a given time bound t. We introduce the notion of worst time of a circuit and show that to d...

Probabilistic modeling of lexicalized grammars is difficult because these grammars exploit complicated data structures, such as typed feature structures. This prevents us from applying common methods of probabilistic modeling in which a complete structure is divided into substructures under the assumption of statistical independence among sub-structures. For example, part-of-speech tagging of a...

The present paper investigates proof-theoretical and algebraic properties for the probability logic FP(Ł,Ł), meant reasoning on uncertainty of Łukasiewicz events. Methodologically speaking, we will consider a translation function between formulas FP(Ł,Ł) to propositional language that allows us apply latter well-developed theory MV-algebras directly probabilistic reasoning. More precisely, leve...

We desribe a variation of the planning domain definition language, PDDL, that permits the modeling of probabilistic planning problems with rewards. This language, PPDDL1.0, was used as the input language for the probabilistic track of the 4th International Planning Competition. We provide the complete syntax for PPDDL1.0 and give a semantics of PPDDL1.0 planning problems in terms of Markov deci...

We define a probabilistic propositional logic for making a finite, ordered sequence of decisions under uncertainty by extending an existing probabilistic propositional logic with expectation and utility-independence formulae. The language has a relatively simple model semantics, and it allows a similarly compact representation of decision problems as influence diagrams. We present a calculus an...

We describe an approach to the automatic generation of convincing jazz melodies using probabilistic grammars. Uses of this approach include a software tool for assisting a soloist in the creation of a jazz solo over chord progressions. The method also shows promise as a means of automatically improvising complete solos in real-time. Our approach has been implemented and demonstrated in a free s...