Brewka, Gerhard


Weighted Abstract Dialectical Frameworks

AAAI Conferences

Abstract 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.


Reactive Multi-Context Systems: Heterogeneous Reasoning in Dynamic Environments

arXiv.org Artificial Intelligence

Managed multi-context systems (mMCSs) allow for the integration of heterogeneous knowledge sources in a modular and very general way. They were, however, mainly designed for static scenarios and are therefore not well-suited for dynamic environments in which continuous reasoning over such heterogeneous knowledge with constantly arriving streams of data is necessary. In this paper, we introduce reactive multi-context systems (rMCSs), a framework for reactive reasoning in the presence of heterogeneous knowledge sources and data streams. We show that rMCSs are indeed well-suited for this purpose by illustrating how several typical problems arising in the context of stream reasoning can be handled using them, by showing how inconsistencies possibly occurring in the integration of multiple knowledge sources can be handled, and by arguing that the potential non-determinism of rMCSs can be avoided if needed using an alternative, more skeptical well-founded semantics instead with beneficial computational properties. We also investigate the computational complexity of various reasoning problems related to rMCSs. Finally, we discuss related work, and show that rMCSs do not only generalize mMCSs to dynamic settings, but also capture/extend relevant approaches w.r.t. dynamics in knowledge representation and stream reasoning.


Solving Advanced Argumentation Problems with Answer-Set Programming

AAAI Conferences

Powerful formalisms for abstract argumentation have been proposed. Their complexity is often located beyond NP and ranges up to the third level of the polynomial hierarchy. The combined complexity of Answer-Set Programming (ASP) exactly matches this complexity when programs are restricted to predicates of bounded arity. In this paper, we exploit this coincidence and present novel efficient translations from abstract dialectical frameworks (ADFs) and GRAPPA to ASP.We also empirically compare our approach to other systems for ADF reasoning and report promising results.


Answer Set Programming: An Introduction to the Special Issue

AI Magazine

This editorial introduces answer set programming, a vibrant research area in computational knowledge representation and declarative programming. We give a brief overview of the articles that form this special issue on answer set programming and of the main topics they discuss.


Answer Set Programming: An Introduction to the Special Issue

AI Magazine

This editorial introduces answer set programming, a vibrant research area in computational knowledge representation and declarative programming. We give a brief overview of the articles that form this special issue on answer set programming and of the main topics they discuss.


AGM Meets Abstract Argumentation: Expansion and Revision for Dung Frameworks

AAAI Conferences

In this paper we combine two of the most important areas of knowledge representation, namely belief revision and (abstract) argumentation. More precisely, we show how AGM-style expansion and revision operators can be defined for Dung's abstract argumentation frameworks (AFs). Our approach is based on a reformulation of the original AGM postulates for revision in terms of monotonic consequence relations for AFs. The latter are defined via a new family of logics, called Dung logics, which satisfy the important property that ordinary equivalence in these logics coincides with strong equivalence for the respective argumentation semantics. Based on these logics we define expansion as usual via intersection of models. We show the existence of such operators. This is far from trivial and requires to study realizability in the context of Dung logics. We then study revision operators. We show why standard approaches based on a distance measure on models do not work for AFs and present an operator satisfying all postulates for a specific Dung logic.


asprin: Customizing Answer Set Preferences without a Headache

AAAI Conferences

In this paper we describe asprin, a general, flexible, and extensible framework for handling preferences among the stable models of a logic program. We show how complex preference relations can be specified through user-defined preference types and their arguments. We describe how preference specifications are handled internally by so-called preference programs, which are used for dominance testing. We also give algorithms for computing one, or all, optimal stable models of a logic program. Notably, our algorithms depend on the complexity of the dominance tests and make use of multi-shot answer set solving technology.


Representing Preferences Among Sets

AAAI Conferences

We study methods to specify preferences among subsets of a set (a universe ). The methods we focus on are of two types. The first one assumes the universe comes with a preference relation on its elements and attempts to lift that relation to subsets of the universe. That approach has limited expressivity but results in orderings that capture interesting general preference principles. The second method consists of developing formalisms allowing the user to specify "atomic" improvements, and generating from them preferences on the powerset of the universe. We show that the particular formalism we propose is expressive enough to capture the lifted preference relations of the first approach, and generalizes propositional CP-nets. We discuss the importance of domain-independent methods for specifying preferences on sets for knowledge representation formalisms, selecting the formalism of argumentation frameworks as an illustrative example.


Abstract Dialectical Frameworks

AAAI Conferences

In this paper we introduce dialectical frameworks, a powerful generalization of Dung-style argumentation frameworks where each node comes with an associated acceptance condition. This allows us to model different types of dependencies, e.g. support and attack, as well as different types of nodes within a single framework. We show that Dung's standard semantics can be generalized to dialectical frameworks, in case of stable and preferred semantics to a slightly restricted class which we call bipolar frameworks. We show how acceptance conditions can be conveniently represented using weights respectively priorities on the links and demonstrate how some of the legal proof standards can be modeled based on this idea.


State Defaults and Ramifications in the Unifying Action Calculus

AAAI Conferences

We present a framework for reasoning about actions that not only solves the frame and ramification problems, but also the state default problem—the problem to determine what normally holds at a given time point. Yet, the framework is general enough not to be tied to a specific time structure. This is achieved as follows: We use effect axioms that draw ideas both from Reiter's successor state axioms and the non-monotonic causal theories by Giunchiglia et al. These axioms are formulated in a recently proposed unifying action calculus to guarantee independence of a specific underlying notion of time. Reiter's default logic is then wrapped around the resulting calculus and plays a key role in solving the ramification as well as the state default problem.