Combining probability and first-order logic has been the subject of intensive research during the last ten years. The most well-known formalisms combining probability and some subset of first-order logic are probabilistic relational models (PRMs), Bayesian logic programs (BLPs) and Markov logic networks (MLNs). Of these three formalisms, MLN is the currently most actively researched. While the ...

This paper aims to extend in two directions the probabilistic dynamic epistemic logic provided in Kooi’s paper [7] and to relate these extensions to ones made in [10]. Kooi’s probabilistic dynamic epistemic logic adds to probabilistic epistemic logic sentences that express consequences of public announcements. The paper [10] extends [7] to using action models, but in both papers, the probabilit...

A significant part of current research on (inductive) logic programming deals with probabilistic logical models. Over the last decade many logics or languages for representing such models have been introduced. There is currently a great need for insight into the relationships between all these languages. One kind of languages are those that extend probabilistic models with elements of logic, su...

Probabilistic inductive logic programming (PILP), sometimes also called statistical relational learning, addresses one of the central questions of artificial intelligence: the integration of probabilistic reasoning with first order logic representations and machine learning. A rich variety of different formalisms and learning techniques have been developed and they are being applied on applicat...

This paper is directed towards an infrastructure for handling both uncertainty and vagueness in the Rules, Logic, and Proof layers of the Semantic Web. More concretely, we present probabilistic fuzzy description logic programs, which combine fuzzy description logics, fuzzy logic programs (with stratified nonmonotonic negation), and probabilistic uncertainty in a uniform framework for the Semant...

In this paper, we propose a new logic for expressing and reasoning about probabilistic hyperproperties. Hyperproperties characterize the relation between different independent executions of a system. Probabilistic hyperproperties express quantitative dependencies between such executions. The standard temporal logics for probabilistic systems, i.e., PCTL and PCTL can refer only to a single path ...

In this paper probabilistic and non-deterministic programs are considered on the ground of logic of programs. We are interested in dependencies between nondeterministic and probabilistic interpretation of a program. The formal definitions of probabilistic and non-deterministic semantics are the starting point for our considerations. The emphasis is on differences in expressibility the halting p...

This paper investigates probabilistic logics endowed with independence relations. We review propositional probabilistic languages without independence, and then consider graph-theoretic representations for propositional probabilistic logic with independence; complexity is analyzed, algorithms are derived, and examples are discussed. Finally, we examine a restricted first order probabilistic log...

A complete and decidable propositional logic for reasoning about states of probabilistic sequential programs is presented. The state logic is then used to obtain a sound Hoare-style calculus for basic probabilistic sequential programs. The Hoare calculus presented herein is the first probabilistic Hoare calculus with a complete and decidable state logic that has truth-functional propositional (...

Reasoning with qualitative and quantitative uncertainty is required in some real-world applications [6]. However, current extensions to logic programming with uncertainty support representing and reasoning with either qualitative or quantitative uncertainty. In this paper we extend the language of Hybrid Probabilistic Logic programs [28, 25], originally introduced for reasoning with quantitativ...