In many applications, the goal is to model the probability distribution of a set of random variables that are related by a causal process, that is, the variables interact through a sequence of nondeterministic or probabilistic events. Causal Probabilistic Logic (CP-logic) (Vennekens et al., 2006) is a probabilistic logic modeling language that can model such processes. The model takes the form ...

We study the problem of reasoning in the probabilistic Description Logic BEL. Using a novel structure, we show that probabilistic reasoning in this logic can be reduced in polynomial time to standard inferences over a Bayesian network. This reduction provides tight complexity bounds for probabilistic reasoning in BEL.

Tabling in logic programming has been used to eliminate redundant computation and also to stop infinite loop. In this paper we investigate another possibility of tabling, i.e. to compute an infinite sum of probabilities for probabilistic logic programs. Using PRISM, a logic-based probabilistic modeling language with a tabling mechanism, we generalize prefix probability computation for probabili...

Employing maximum entropy methods on probabilistic conditional logic has proven to be a useful approach for commonsense reasoning. Yet, the expressive power of this logic and similar formalisms is limited due to their foundations on propositional logic and in the past few years a lot of proposals have been made for probabilistic reasoning in relational settings. Most of these proposals rely on ...

The representation of uncertainty in the semantic web can be eased by the use of learning techniques. To completely induce a probabilistic ontology (that is, an ontology encoded through a probabilistic description logic) from data, two basic tasks must be solved: (1) learning concept definitions and (2) learning probabilistic inclusions. In this paper we propose and test an algorithm that learn...

We represent natural language semantics by combining logical and distributional information in probabilistic logic. We use Markov Logic Networks (MLN) for the RTE task, and Probabilistic Soft Logic (PSL) for the STS task. The system is evaluated on the SICK dataset. Our best system achieves 73% accuracy on the RTE task, and a Pearson’s correlation of 0.71 on the STS task.

We propose a uniform semantic framework for interpreting probabilistic concept subsumption and probabilistic role quantification through statistical sampling distributions. This general semantic principle serves as the foundation for the development of a probabilistic version of the guarded fragment of first-order logic. A characterization of equivalence in that logic in terms of bisimulations ...

This paper presents an application of an optimized implementation of a probabilistic description logic defined by Giugno and Lukasiewicz [9] to the domain of image interpretation. This approach extends a description logic with so-called probabilistic constraints to allow for automated reasoning over formal ontologies in combination with probabilistic knowledge. We analyze the performance of cur...

We survey three applications of mathematical programming to rea soning under uncertainty a an application of linear programming to probabilistic logic b an application of nonlinear programming to Bayesian logic a combination of Bayesian inference with probabilistic logic and c an application of integer programming to Dempster Shafer theory which is a method of combining evidence from di erent s...

The probability theory is a well-studied branch of mathematics, in order to carry out formal reasoning about probability. Thus, it is important to have a logic, both for computation of probabilities and for reasoning about probabilities, with a well-defined syntax and semantics. Both current approaches, based on Nilsson’s probability structures/logics, and on linear inequalities in order to rea...