We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore the relationship between coherence-based and classical 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 reas...

While grasps must satisfy the grasping stability criteria, good grasps depend on the specific manipulation scenario: the object, its properties and functionalities, as well as the task and grasp constraints. In this paper, we consider such information for robot grasping by leveraging manifolds and symbolic object parts. Specifically, we introduce a new probabilistic logic module to first semant...

Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. Several classical probabilistic inference tasks (such as MAP and computing marginals) have not yet received a lot of attention for this formalism. The contribution of this paper is that we develop efficient inference algorithms for these tasks. This is based on a conversion of the probab...

Preface The past several 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-bas...

The probabilistic modal μ-calculus is a fixed-point logic designed for expressing properties of probabilistic labeled transition systems (PLTS’s). Two equivalent semantics have been studied for this logic, both assigning to each state a value in the interval [0, 1] representing the probability that the property expressed by the formula holds at the state. One semantics is denotational and the o...

Let L be some extension of classical propositional logic. The noniterated probabilistic logic over L, is the logic PL that is defined by adding non-nested probabilistic operators in the language of L. For example in PL we can express a statement like “the probability of truthfulness of A is at 0.3” where A is a formula of L. The iterated probabilistic logic over L is the logic PPL, where the pr...

In the past ten years, the areas of probabilistic inductive logic programming and statistical relational learning put forth a large collection of approaches to combine relational representations of knowledge with probabilistic reasoning. Here, we develop a series of evaluation and comparison criteria for those approaches and focus on the point of view of knowledge representation and reasoning. ...

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...

Many machine learning applications require the ability to learn from and reason about noisy multi-relational data. To address this, several effective representations have been developed that provide both a language for expressing the structural regularities of a domain, and principled support for probabilistic inference. In addition to these two aspects, however, many applications also involve ...