Gerhard Brewka

Answer set programming at a glance

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

Preferred answer sets for extended logic programs

Abstract In this paper, we address the issue of how Gelfond and Lifschitzs 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.

Cumulative default logic: in defense of nonmonotonic inference rules

Abstract Two problems of Reiters default logic have recently been discussed in the literature: first, inconsistencies between justifications of nonnormal defaults may lead to unintuitive results, and second, default logic is not cumulative, i.e., the addition of theorems to the set of premises may change the derivable formulas. To solve these two problems we strengthen the applicability condition for defaults and make the reasons for believing something an explicit part of the derived formulas. The resulting new logic turns out to be semi-monotonic. If the additional expressiveness of nonnormal defaults is to be retained only some of the extensions of this logic are to be taken as acceptable sets of beliefs, however: those preserving priorities between defaults.

Dynamic Argument Systems: A Formal Model of Argumentation Processes Based on Situation Calculus

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 Reschers theory of formal disputation and a dynamic argument system with three levels which we use to discuss a murder case.

Qualitative choice logic

Qualitative choice logic (QCL) is a propositional logic for representing alternative, ranked options for problem solutions. The logic adds to classical propositional logic a new connective called ordered disjunction: A ×→ B intuitively means: if possible A, but if A is not possible then at least B. The semantics of qualitative choice logic is based on a preference relation among models. Consequences of QCL theories can be computed through a compilation to stratified knowledge bases which in turn can be compiled to classical propositional theories. We also discuss potential applications of the logic, several variants of QCL based on alternative inference relations, and their relation to existing nonmonotonic formalisms.

KI 2001: Advances in Artificial Intelligence

There has been growing interest in AI and related disciplines in the emerging field of computational game theory. This area revisits the problems and solutions of classical game theory with an explicit emphasis on computational efficiency and scalability. The interest from the AI community arises from several sources, including models and algorithms for multi-agent systems, design of electronic commerce agents, and the study of compact representations for complex environments that permit efficient learning and planning algorithms. In the talk, I will survey some recent results in computational game theory, and highlight similarities with algorithms, representations and motivation in the AI and machine learning literature. The topics examined will include a simple study of gradient algorithms in general games [1], the application of reinforcement learning algorithms and their generalizations to stochastic games [2], and the introduction of compact graphical models for multi-player games [3,4]. Interesting directions for further work will be discussed.

Prioritizing Default Logic

In nonmonotonic reasoning conflicts among defaults are ubiquitous. For instance, more specific rules may be in conflict with more general ones, a problem which has been studied intensively in the context of inheritance networks (Poole, 1985; Touretzky, 1986; Touretzky et al., 1991). When defaults are used for representing design goals in configuration tasks conflicts naturally arise. The same is true in model based diagnosis where defaults are used to represent the assumption that components typically are ok. In legal reasoning conflicts among rules are very common (Prakken, 1993) and keep many lawyers busy (and rich).

Managed multi-context systems

Multi-context systems (MCS) are a powerful framework for interlinking heterogeneous knowledge sources. They model the flow of information among different reasoning components (called contexts) in a declarative way, using so-called bridge rules, where contexts and bridge rules may be nonmonotonic. We considerably generalize MCS to managed MCS (mMCS): while the original bridge rules can only add information to contexts, our generalization allows arbitrary operations on context knowledge bases to be freely defined, e.g., deletion or revision operators. The paper motivates and introduces the generalized framework and presents several interesting instances. Furthermore, we consider inconsistency management in mMCS and complexity issues.

Implementing Ordered Disjunction Using Answer Set Solvers for Normal Programs

Logic programs with ordered disjunction (LPODs) add a new connective to logic programming. This connective allows us to represent alternative, ranked options for problem solutions in the heads of rules: A × B intuitively means: 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. In this paper 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.

Logic Programs with Ordered Disjunction

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.