We study probabilistic complexity classes and questions of derandomisation from a logical point of view. For each logic L we introduce a new logic BPL, bounded error probabilistic L, which is defined from L in a similar way as the complexity class BPP, bounded error probabilistic polynomial time, is defined from P. Our main focus lies on questions of derandomisation, and we prove that there is ...

This paper analyzes the probabilistic description logic P-SHIQ as a fragment of first-order probabilistic logic (FOPL). P-SHIQ was suggested as a language that is capable of representing and reasoning about different kinds of uncertainty in ontologies, namely generic probabilistic relationships between concepts and probabilistic facts about individuals. However, some semantic properties of P-SH...

We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore the relationship between coherencebased and model-theoretic probabilistic logic. Interestingly, we show that the notions of g-coherence and of g-coherent entailment can be expressed by combining notions in model-theoretic probabilistic logic with concepts from default reasoning. Cruc...

In previous work, we have introduced probabilistic description logic programs for the Semantic Web, which combine description logics, normal programs under the answer set (resp., well-founded) semantics, and probabilistic uncertainty. In this paper, we continue this line of research. We propose an approach to probabilistic data integration for the Semantic Web that is based on probabilistic des...

Larsen and Skou characterized probabilistic bisimilarity over reactive probabilistic systems with a logic including true, negation, conjunction, and a diamond modality decorated with a probabilistic lower bound. Later on, Desharnais, Edalat, and Panangaden showed that negation is not necessary to characterize the same equivalence. In this paper, we prove that the logical characterization holds ...

Speciications for probabilistic programs often use the notion of almost always and deenitely sometime to capture the probabilistic information. But there are a number of instances (eg. network protocols) where probabilistic information needs to be explicitly speciied. In this paper we present PCTL , a probabilistic version of the branching time logic CTL , where the quantiiers for universality ...

The probabilistic fuzzy set (PFS) and the related probabilistic fuzzy logic system (PFLS) is designed for handling the uncertainties in both stochastic and nonstochastic nature. In this paper, a bell-shaped probabilistic fuzzy set is proposed and the related PFLS is constructed and applied to a modeling problem to study stochastic modeling capability. It clearly discloses that the bell-shaped P...

Probabilistic team semantics is a framework for logical analysis of probabilistic dependencies. Our focus on the axiomatizability, complexity, and expressivity inclusion logic its extensions. We identify natural fragment existential second-order with additive real arithmetic that captures exactly logic. furthermore relate these formalisms to linear programming, doing so obtain PTIME data comple...

In [12], Nilsson proposed the probabilistic logic in which the truth values of logical propositions are probability values between 0 and 1. It is applicable to any logical system for which the consistency of a finite set of propositions can be established. The probabilistic inference scheme reduces to the ordinary logical inference when the probabilities of all propositions are either 0 or 1. T...

Preface The past few years have witnessed a tremendous interest in logic-based probabilistic learning as testified by the number of formalisms and systems and their applications. Logic-based probabilistic learning is a multidisciplinary research area that integrates relational or logic formalisms, probabilistic reasoning mechanisms, and machine learning and data mining principles. Logic-based p...