Johannes Peter Wallner

Complexity-sensitive decision procedures for abstract argumentation

Abstract argumentation frameworks (AFs) provide the basis for various reasoning problems in the areas of Knowledge Representation and Artificial Intelligence. Efficient evaluation of AFs has thus been identified as an important research challenge. So far, implemented systems for evaluating AFs have either followed a straight-forward reduction-based approach or been limited to certain tractable classes of AFs. In this work, we present a generic approach for reasoning over AFs, based on the novel concept of complexity-sensitivity. Establishing the theoretical foundations of this approach, we derive several new complexity results for preferred, semi-stable and stage semantics which complement the current complexity landscape for abstract argumentation, providing further understanding on the sources of intractability of AF reasoning problems. The introduced generic framework exploits decision procedures for problems of lower complexity whenever possible. This allows, in particular, instantiations of the generic framework via harnessing in an iterative way current sophisticated Boolean satisfiability (SAT) solver technology for solving the considered AF reasoning problems. First experimental results show that the SAT-based instantiation of our novel approach outperforms existing systems.

Methods for solving reasoning problems in abstract argumentation - A survey

Within the last decade, abstract argumentation has emerged as a central field in Artificial Intelligence. Besides providing a core formalism for many advanced argumentation systems, abstract argumentation has also served to capture several non-monotonic logics and other AI related principles. Although the idea of abstract argumentation is appealingly simple, several reasoning problems in this formalism exhibit high computational complexity. This calls for advanced techniques when it comes to implementation issues, a challenge which has been recently faced from different angles. In this survey, we give an overview on different methods for solving reasoning problems in abstract argumentation and compare their particular features. Moreover, we highlight available state-of-the-art systems for abstract argumentation, which put these methods to practice.

The Fourth Answer Set Programming Competition: Preliminary Report

Answer Set Programming is a well-established paradigm of declarative programming in close relationship with other declarative formalisms such as SAT Modulo Theories, Constraint Handling Rules, PDDL and many others. Since its first informal editions, ASP systems are compared in the nowadays customary ASP Competition. The fourth ASP Competition, held in 2012/2013, is the sequel to previous editions and it was jointly organized by University of Calabria Italy and the Vienna University of Technology Austria. Participants competed on a selected collection of benchmark problems, taken from a variety of research areas and real world applications. The Competition featured two tracks: the Model& Solve Track, held on an open problem encoding, on an open language basis, and open to any kind of system based on a declarative specification paradigm; and the System Track, held on the basis of fixed, public problem encodings, written in a standard ASP language.

Analyzing the computational complexity of abstract dialectical frameworks via approximation fixpoint theory

Abstract dialectical frameworks (ADFs) have recently been proposed as a versatile generalization of Dungs abstract argumentation frameworks (AFs). In this paper, we present a comprehensive analysis of the computational complexity of ADFs. Our results show that while ADFs are one level up in the polynomial hierarchy compared to AFs, there is a useful subclass of ADFs which is as complex as AFs while arguably offering more modeling capacities. As a technical vehicle, we employ the approximation fixpoint theory of Denecker, Marek and Truszczynski, thus showing that it is also a useful tool for complexity analysis of operator-based semantics.

Making Use of Advances in Answer-Set Programming for Abstract Argumentation Systems

Dung’s famous abstract argumentation frameworks represent the core formalism for many problems and applications in the field of argumentation which significantly evolved within the last decade. Recent work in the field has thus focused on implementations for these frameworks, whereby one of the main approaches is to use Answer-Set Programming (ASP). While some of the argumentation semantics can be nicely expressed within the ASP language, others required rather cumbersome encoding techniques. Recent advances in ASP systems, in particular, the metasp optimization front-end for the ASP-package gringo/claspD provide direct commands to filter answer sets satisfying certain subset-minimality (or -maximality) constraints. This allows for much simpler encodings compared to the ones in standard ASP language. In this paper, we experimentally compare the original encodings (for the argumentation semantics based on preferred, semi-stable, and respectively, stage extensions) with new metasp encodings. Moreover, we provide novel encodings for the recently introduced resolution-based grounded semantics. Our experimental results indicate that the metasp approach works well in those cases where the complexity of the encoded problem is adequately mirrored within the metasp approach.

On the relation between SPARQL1.1 and Answer Set Programming

Abstract In the context of the emerging Semantic Web and the quest for a common logical framework underpinning its architecture, the relation of rule-based languages such as Answer Set Programming (ASP) and ontology languages such as the Web Ontology Language (OWL) has attracted a lot of attention in the literature over the past years. With its roots in Deductive Databases and Datalog though, ASP shares much more commonality with another Semantic Web standard, namely the Simple Protocol and RDF Query Language (SPARQL). In this paper, we take the recent approval of the SPARQL1.1 standard by the World Wide Web consortium (W3C) as an opportunity to introduce this standard to the Logic Programming community by providing a translation of SPARQL1.1 into ASP. In this translation, we explain and highlight peculiarities of the new W3C standard. Along the way, we survey existing literature on foundations of SPARQL and SPARQL1.1, and also combinations of SPARQL with ontology and rules languages. Thereby, apart from providing the means to implement and support SPARQL natively within Logic Programming engines and particularly ASP engines, we hope to pave the way for further research on a common logical framework for Semantic Web languages, including query languages, from an ASP point of view.

Advanced SAT Techniques for Abstract Argumentation

In the area of propositional satisfiability SAT, tremendous progress has been made in the last decade. Todays SAT technology covers not only the standard SAT problem, but also extensions thereof, such as computing a backbone the literals which are true in all satisfying assignments or minimal corrections sets minimal subsets of clauses which if dropped leave an originally unsatisfiable formula satisfiable. In this work, we show how these methods can be applied to solve important problems from the area of abstract argumentation. In particular, we present new systems for semi-stable, ideal, and eager semantics. Our experimental results demonstrate the feasibility of this approach.

Complexity results and algorithms for extension enforcement in abstract argumentation

Understanding the dynamics of argumentation frameworks (AFs) is important in the study of argumentation in AI. In this work, we focus on the so-called extension enforcement problem in abstract argumentation. We provide a nearly complete computational complexity map of fixed-argument extension enforcement under various major AF semantics, with results ranging from polynomial-time algorithms to completeness for the second-level of the polynomial hierarchy. Complementing the complexity results, we propose algorithms for NP-hard extension enforcement based on constrained optimization. Going beyond NP, we propose novel counterexample-guided abstraction refinement procedures for the second-level complete problems and present empirical results on a prototype system constituting the first approach to extension enforcement in its generality.

Admissibility in the Abstract Dialectical Framework

The aim of this paper is to study the concept of admissibility in abstract dialectical frameworks ADFs. While admissibility is well-understood in Dung-style frameworks, a generalization to ADFs is not trivial. Indeed, the original proposal turned out to behave unintuitively at certain instances. A recent approach circumvented this problem by using a three-valued concept. In this paper, we propose a novel two-valued approach which more directly follows the original understanding of admissibility. We compare the two approaches and show that they behave differently on certain ADFs. Our results imply that for generalizations of Dung-style frameworks, establishing a precise correspondence between two-valued i.e. extension-based and three-value i.e. labeling-based characterizations of argumentation semantics is not easy and requires further investigations.

Synthesizing Argumentation Frameworks from Examples

Argumentation is today a topical area of artificial intelligence (AI) research. Abstract argumentation, with argumentation frameworks (AFs) as the underlying knowledge representation formalism, is a central viewpoint to argumentation in AI. Indeed, from the perspective of AI and computer science, understanding computational and representational aspects of AFs is key in the study of argumentation. Realizability of AFs has been recently proposed as a central notion for analyzing the expressive power of AFs under different semantics. In this work, we propose and study the AF synthesis problem as a natural extension of realizability, addressing some of the shortcomings arising from the relatively stringent definition of realizability. In particular, realizability gives means of establishing exact conditions on when a given collection of subsets of arguments has an AF with exactly the given collection as its set of extensions under a specific argumentation semantics. However, in various settings within the study of dynamics of argumentation—including revision and aggregation of AFs—non-realizability can naturally occur. To accommodate such settings, our notion of AF synthesis seeks to construct, or synthesize, AFs that are semantically closest to the knowledge at hand even when no AFs exactly representing the knowledge exist. Going beyond defining the AF synthesis problem, we study both theoretical and practical aspects of the problem. In particular, we (i) prove NP-completeness of AF synthesis under several semantics, (ii) study basic properties of the problem in relation to realizability, (iii) develop algorithmic solutions to NP-hard AF synthesis using the constraint optimization paradigms of maximum satisfiability and answer set programming, (iv) empirically evaluate our algorithms on different forms of AF synthesis instances, as well as (v) discuss variants and generalizations of AF synthesis.