Hannes Strass

Approximating operators and semantics for abstract dialectical frameworks

We provide a systematic in-depth study of the semantics of abstract dialectical frameworks (ADFs), a recent generalisation of Dung@?s abstract argumentation frameworks. This is done by associating with an ADF its characteristic one-step consequence operator and defining various semantics for ADFs as different fixpoints of this operator. We first show that several existing semantical notions are faithfully captured by our definition, then proceed to define new ADF semantics and show that they are proper generalisations of existing argumentation semantics from the literature. Most remarkably, this operator-based approach allows us to compare ADFs to related nonmonotonic formalisms like Dung argumentation frameworks and propositional logic programs. We use polynomial, faithful and modular translations to relate the formalisms, and our results show that both abstract argumentation frameworks and abstract dialectical frameworks are at most as expressive as propositional normal logic programs.

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.

Summary Report of The First International Competition on Computational Models of Argumentation

We review the First International Competition on Computational Models of Argumentation (ICMMA’15). The competition evaluated submitted solvers performance on four different computational tasks related to solving abstract argumentation frameworks. Each task evaluated solvers in ways that pushed the edge of existing performance by introducing new challenges. Despite being the first competition in this area, the high number of competitors entered, and differences in results, suggest that the competition will help shape the landscape of ongoing developments in argumentation theory solvers.

Instantiating Knowledge Bases in Abstract Dialectical Frameworks

We present a translation from defeasible theory bases to abstract dialectical frameworks, a recent generalisation of abstract argumentation frameworks. Using several problematic examples from the literature, we first show how our translation addresses important issues of existing approaches. We then prove that the translated frameworks satisfy the rationality postulates closure and direct/indirect consistency. Furthermore, the frameworks can detect inconsistencies in the set of strict inference rules and cyclic strict and defeasible supports amongst literals. We also show that the translation involves at most a quadratic blowup and is therefore effectively and efficiently computable.

Compact argumentation frameworks

Abstract argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are characterized by the feature that each argument of the AF occurs in at least one extension. This not only guarantees a certain notion of fairness; compact AFs are thus also minimal in the sense that no argument can be removed without changing the outcome. We address the following questions in the paper: (1) How are the classes of compact AFs related for different semantics? (2) Under which circumstances can AFs be transformed into equivalent compact ones? (3) Finally, we show that compact AFs are indeed a non-trivial subclass, since the verification problem remains coNP-hard for certain semantics.

A Benchmark Framework for a Computational Argumentation Competition

We introduce probo, a general benchmark framework for comparing abstract argumentation solvers. probo is intended to act as the core of an argumentation competition intended to run in 2015.

On the Maximal and Average Numbers of Stable Extensions

We present an analytical and empirical study of the maximal and average numbers of stable extensions in abstract argumentation frameworks. As one of the analytical main results, we prove a tight upper bound on the maximal number of stable extensions that depends only on the number of arguments in the framework. More interestingly, our empirical results indicate that the distribution of stable extensions as a function of the number of attacks in the framework seems to follow a universal pattern that is independent of the number of arguments.

Instantiating rule-based defeasible theories in abstract dialectical frameworks and beyond

dialectical frameworks and beyond

A general first-order solution to the ramification problem with cycles

Abstract We provide a solution to the ramification problem that integrates findings of different axiomatic approaches to ramification from the last ten to fifteen years. For the first time, we present a solution that: (1) is independent of a particular time structure, (2) is formulated in classical first-order logic, (3) treats cycles – a notoriously difficult aspect – properly, and (4) is assessed against a state-transition semantics via a formal correctness proof. This is achieved as follows: We introduce indirect effect laws that enable us to specify ramifications that are triggered by activation of a formula rather than just an atomic effect. We characterise the intended models of these indirect effect laws by a state-transition semantics. Afterwards, we show how to compile a class of indirect effect laws into first-order effect axioms that then solve the ramification and frame problems. We finally prove the resulting effect axioms sound and complete with respect to the semantics defined earlier.

A language for default reasoning about actions

Action languages allow for a concise representation of actions and their effects while at the same time being easily readable and writable for humans. In this paper, we introduce