The motivation and key concepts behind answer set programming---a promising approach to declarative problem solving.

In this paper, we address the issue of how Gelfond and Lifschitz's answer set semantics for extended logic programs can be suitably modified to handle prioritized programs. In such programs an ordering on the program rules is used to express preferences. We show how this ordering can be used to define preferred answer sets and thus to increase the set of consequences of a program. We define a strong and a weak notion of preferred answer sets. The first takes preferences more seriously, while the second guarantees the existence of a preferred answer set for programs possessing at least one answer set. Adding priorities to rules is not new, and has been explored in different contexts. However, we show that many approaches to priority handling, most of which are inherited from closely related formalisms like default logic, are not suitable and fail on intuitive examples. Our approach, which obeys abstract, general principles that any approach to prioritized knowledge representation should satisfy, handles them in the expected way. Moreover, we investigate the complexity of our approach. It appears that strong preference on answer sets does not add on the complexity of the principal reasoning tasks, and weak preference leads only to a mild increase in complexity.

Logic programs with ordered disjunction (LPODs) contain a new connective which allows representing alternative, ranked options for problem solutions in the heads of rules: A × B intuitively means that if possible A, but if A is not possible, then at least B. The semantics of logic programs with ordered disjunction is based on a preference relation on answer sets. We show how LPODs can be implemented using answer set solvers for normal programs. The implementation is based on a generator, which produces candidate answer sets and a tester which checks whether a given candidate is maximally preferred and produces a better candidate if it is not. We also discuss the complexity of reasoning tasks based on LPODs and possible applications.

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We present a formal model of argumentation based on situation calculus which captures both the logical and the procedural aspects of argumentation processes. The logic is used to determine what is accepted by each agent participating in the discussion and by the group as a whole, on the basis of the speech acts performed during argumentation. Argumentation protocols, also called rules of order, describe declaratively which speech acts are legal in a particular state of the argumentation. We rst discuss argumentation with xed rules of order. Our model tolerates protocol violations but makes it possible to object to illegal actions. In realistic settings the rules of order themselves can at any time become the topic of the debate. We show how meta level argumentation of this kind can be modelled in what we call dynamic argument systems. To illustrate the notions introduced in the paper we present a reconstruction of Rescher's theory of formal disputation and a dynamic argument system with three levels which we use to discuss a murder case.

Dialectical Frameworks (ADFs) generalize Dung's argumentation frameworks allowing various relationships among arguments to be expressed in a systematic way. We further generalize ADFs so as to accommodate arbitrary acceptance degrees for the arguments. This makes ADFs applicable in domains where both the initial status of arguments and their relationship are only insufficiently specified by Boolean functions. We define all standard ADF semantics for the weighted case, including grounded, preferred and stable semantics. We illustrate our approach using acceptance degrees from the unit interval and show how other valuation structures can be integrated. In each case it is sufficient to specify how the generalized acceptance conditions are represented by formulas, and to specify the information ordering underlying the characteristic ADF operator. We also present complexity results for problems related to weighted ADFs.

The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This is achieved by using a reserved predicate symbol and a naming technique. Con icts among rules are resolved whenever possible on the basis of derived preference information. The well-founded conclusions of prioritized logic programs can be computed in polynomial time. A legal reasoning example illustrates the usefulness of the approach.