The semantic characterization of answer sets as classical models of a logic program satisfying all loop formulas, due to Lin and Zhao [2004], showed that answer sets can be understood as solutions to a set of (Boolean) constraints. This observation has led to the development of answer set solvers that exploit solvers for classical propositional logic as back-end inference engines. Recently, our group in Potsdam developed the new answer set solver "clasp", also relying on (Boolean) constraints, e.g. in backjumping and conflict-driven learning, which are some of the key techniques natively supported within "clasp". To our knowledge, "clasp" is the first and sill the only answer set solver that combines answer set and (Boolean) constraint solving techniques in an efficient way. The talk introduces the semantic basis of "clasp", its disjunctive spin-off "claspD", and finally, we consider related issues arising in answer set programming, like grounding and incrementality.

• Thematic program: Foundations of Knowledge and Information Handling (2007)
• Thematic program: Foundations of Knowledge and Information Handling (2007)

If-then rules, which are arguably the most common form of knowledge representation in Artificial Intelligence, are ambiguous. They can be interpreted both as logic programs having the form if conditions then conclusions and as production rules having the form if conditions then do actions. The relationship between these different kinds of rules has received little attention in the AI literature, and, when it has, different authors have reached entirely different conclusions. Some authors, such as Russell and Norvig in their textbook Introduction to Artificial Intelligence, view production rules as just logical implications used to reason forward, while Herbert Simon in the MIT Encyclopedia of Cognitive Science views the logic programming language Prolog as one of many production system languages. On the other hand, Thagard in his Introduction to Cognitive Science denies any relationship between logic and production rules at all. In this talk, I will explore the relationships between logic programs and production rules and propose a framework that combines the two kinds of rules and eliminates the overlap between them. The framework uses production rules for sentences of the form if conditions then achieve goals, and it uses logic programs both to evaluate conditions and to achieve goals by reducing goals to sub-goals. I will discuss the problems of giving the resulting framework both a declarative, model-theoretic semantics and an operational semantics in the form of a transition system.

• Thematic program: Foundations of Knowledge and Information Handling (2007)

n this talk I will consider computational problems that (A) can be solved in polynomial time for graphs of bounded treewidth and (B) where the order of the polynomial time bound is expected to depend on the treewidth of the instance. Among the considered problems are coloring problems, factor problems, orientation problems and satisfiability problems. I will present an algorithmic meta-theorem (an extension of Courcelle's Theorem) that provides a convenient way for establishing (A) for some of the considered problems and I will explain how concepts from parameterized complexity theory can be used to establish (B).

• Thematic program: Foundations of Knowledge and Information Handling (2007)

In this paper we introduce a modular framework for abstract argumentation where the argumentation context, that is information about preferences among arguments, values, validity, reasoning mode (skeptical vs. credulous) and even the chosen semantics can be explicitly represented. The framework consists of a collection of abstract argument systems connected via mediators. The mediators integrate information coming from connected argument systems - possibly solving conflicts within this information - and provide the context used in a particular argumentation module. We show how the framework can be used for hierarchic argumentation as typically found in legal reasoning, and we show how it can be used to model group argumentation processes.

• Thematic program: Foundations of Knowledge and Information Handling (2007)

In order to establish a theoretical foundation for database transformations, a universal computation model as an umbrella for queries and updates is needed. As updates are fundamentally distinct from queries in many respects, computation models for queries cannot be simply extended to database transformations. This motivates the question whether Abstract State Machines (ASMs) can be used to characterize database transformations in general. In the talk I will start examining the differences between database transformations and algorithms, which give rise to the formalization of of five postulates for database transformations. Then a variant of ASMs called Abstract Database Transformations Machines (ASTMs) is developed, and I will sketch the proof that ADTMs capture database transformations, i.e. the main result is that every database transformation stipulated by the postulates can be behaviorally simulated by an ADTM.

• Thematic program: Foundations of Knowledge and Information Handling (2007)