We look at probabilistic logic programs as a specification language for probabilistic models, and study their interpretation and complexity. Acyclic programs specify Bayesian networks, and, depending on constraints on logical atoms, their inferential complexity reaches complexity classes #P, #NP, and even #EXP. We also investigate (cyclic) stratified probabilistic logic programs, showing that t...

Probabilistic logics have attracted a great deal of attention during the past few years. While logical languages have taken a central position in research on knowledge representation and automated reasoning, probabilistic graphical models with their probabilistic basis have taken up a similar position when it comes to reasoning with uncertainty. The formalism of chain graphs is increasingly see...

In this paper I combine the dynamic epistemic logic of Gerbrandy (1999) with the probabilistic logic of Fagin and Halpern (1994). The result is a new probabilistic dynamic epistemic logic, a logic for reasoning about probability, information, and information change that takes higher order information into account. Probabilistic epistemic models are defined, and a way to build them for applicati...

2 Knowledge Representation and Reasoning (1p) 3 2.1 Logic and Combinatorics (1p) . . . . . . . . . . . . . . . . . . . . 4 2.1.1 Propositional Reasoning and Constraints Satisfaction (1p) 4 2.1.2 First-Order Logic and Its Restrictions (1.5p) . . . . . . . 5 2.1.3 Knowledge, Belief, Agents, and Modal Logic (0.75p) . . . 6 2.1.4 Logic Programming, Nonmonotonic Reasoning, and Preferences (0.75p) . ...

We introduce probabilistic regular tree expressions and give a Kleene-like theorem for probabilistic tree automata (PTA). Furthermore, we define probabilistic MSO logic. This logic is more expressive than PTA. We define bottom-up PTA, which are strictly more expressive than PTA. Using bottom-up PTA, we prove a Büchi-like theorem for probabilistic MSO logic. We obtain a Nivat-style theorem as an...

Probabilistic inductive logic programming, 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. In the present paper, we start from inductiv...

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 technical report describes the usage, syntax, semantics and core algorithms of the probabilistic inductive logic programming framework PrASP. PrASP is a research software which integrates non-monotonic reasoning based on Answer Set Programming (ASP), probabilistic inference and parameter learning. In contrast to traditional approaches to Probabilistic (Inductive) Logic Programming, our fra...

In recent years, there has been a significant interest in integrating probability theory with first order logic and relational representations [see De Raedt and Kersting, 2003, for an overview]. Muggleton [1996] and Cussens [1999] have upgraded stochastic grammars towards Stochastic Logic Programs, Sato and Kameya [2001] have introduced Probabilistic Distributional Semantics for logic programs,...

Reasoning with inaccurate information is a major topic within the fields of artificial intelligence in general and knowledge representation and reasoning in particular. This thesis deals with information that can be incomplete, uncertain, and contradictory. We employ probabilistic conditional logic as a foundation for our investigation. This framework allows for the representation of uncertain ...