Current literature offers a number of different approaches to what could generally be called "probabilistic logic programming". These are usually based on Horn clauses. Here, we introduce a new formalism, Logic Programs with Annotated Disjunctions, based on disjunctive logic programs. In this formalism, each of the disjuncts in the head of a clause is annotated with a probability. Viewing such a set of probabilistic disjunctive clauses as a probabilistic disjunction of normal logic programs allows us to derive a possible world semantics, more precisely, a probability distribution on the set of all Herbrand interpretations. We demonstrate the strength of this formalism by some examples and compare it to related work.

We examine the relation between constructive processes and the concept of causality. We observe that causality has an inherent dynamic aspect, i.e., that, in essence, causal information concerns the evolution of a domain over time. Motivated by this observation, we construct a new representation language for causal knowledge, whose semantics is defined explicitly in terms of constructive processes. This is done in a probabilistic context, where the basic steps that make up the process are allowed to have non-deterministic effects. We then show that a theory in this language defines a unique probability distribution over the possible outcomes of such a process. This result offers an appealing explanation for the usefulness of causal information and links our explicitly dynamic approach to more static causal probabilistic modeling languages, such as Bayesian networks. We also show that this language, which we have constructed to be a natural formalization of a certain kind of causal statements, is closely related to logic programming. This result demonstrates that, under an appropriate formal semantics, a rule of a normal, a disjunctive or a certain kind of probabilistic logic program can be interpreted as a description of a causal event.

This paper reports on the Second Answer Set Programming Competition. The competitions in areas of Satisfiability checking, Pseudo-Boolean constraint solving and Quantified Boolean Formula evaluation have proven to be a strong driving force for a community to develop better performing systems. Following this experience, the Answer Set Programming competition series was set up in 2007, and ran as part of the International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR). This second competition, held in conjunction with LPNMR 2009, differed from the first one in two important ways. First, while the original competition was restricted to systems designed for the answer set programming language, the sequel was open to systems designed for other modeling languages, as well. Consequently, among the contestants of the second competition were a CLP(FD) team and three model generation systems for (extensions of) classical logic. Second, this latest competition covered not only satisfiability problems but also optimization ones. We present and discuss the set-up and the results of the competition.

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argumentation Abstract dialectical frameworks In various domains of logic, researchers have made use of a similar intuition: that facts (or models) can be derived from the ground up. They typically phrase this intuition by saying, e.g., that the facts should be grounded, or that they should not be unfounded, or that they should be supported by cycle-free arguments, et cetera. In this paper, we formalise this intuition in the context of algebraical fixpoint theory. We define when a lattice element x ∈ L is grounded for lattice operator O : L → L. On the algebraical level, we investigate the relationship between grounded fixpoints and the various classes of fixpoints of approximation fixpoint theory, including supported, minimal, Kripke-Kleene, stable and well-founded fixpoints. On the logical level, we investigate groundedness in the context of logic programming, autoepistemic logic, default logic and argumentation frameworks. We explain what grounded points and fixpoints mean in these logics and show that this concept indeed formalises intuitions that existed in these fields. We investigate which existing semantics are grounded. We study the novel semantics for these logics that is induced by grounded fixpoints, which has some very appealing properties, not in the least its mathematical simplicity and generality. Our results unveil a remarkable uniformity in intuitions and mathematics in these fields.

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Abstract. We study causal information about probabilistic processes, i.e., information about why events occur. A language is developed in which such information can be formally represented and we investigate when this suffices to uniquely characterize the probability distribution that results from such a process. We examine both detailed representations of temporal aspects and representations in which time is implicit. In this last case, our logic turns into a more fine-grained version of Pearl's approach to causality. We relate our logic to certain probabilistic logic programming languages, which leads to a clearer view on the knowledge representation properties of these language. We show that our logic induces a semantics for disjunctive logic programs, in which these represent non-deterministic processes. We show that logic programs under the well-founded semantics can be seen as a language of deterministic causality, which we relate to McCain & Turner's causal theories.

Abstract. This paper presents a Knowledge Base project for FO(ID), an extension of classical logic with inductive definitions. This logic is a natural integration of classical logic and logic programming based on the view of a logic program as a definition. We discuss the relationship between inductive definitions and common sense reasoning and the strong similarities and striking differences with ASP and Abductive LP. We report on inference systems that combine state-of-the-art techniques of SAT and ASP. Experiments show that FO(ID) model expansion systems are competitive with the best ASP-solvers.