This paper is a contribution to the research on dynamics in assumption-based argumentation (ABA). We investigate situations where a given knowledge base undergoes certain changes. We show that two frequently investigated problems, namely enforcement of a given target atom and deciding strong equivalence of two given ABA frameworks, are intractable in general. Notably, these problems are both tractable for abstract argumentation frameworks (AFs) which admit a close correspondence to ABA by constructing semanticspreserving instances. Inspired by this observation, we search for tractable fragments for ABA frameworks by means of the instantiated AFs. We argue that the usual instantiation procedure is not suitable for the investigation of dynamic scenarios since too much information is lost when constructing the abstract framework. We thus consider an extension of AFs, called cvAFs, equipping arguments with conclusions and vulnerabilities in order to better anticipate their role after the underlying knowledge base is extended. We investigate enforcement and strong equivalence for cvAFs and present syntactic conditions to decide them. We show that the correspondence between cvAFs and ABA frameworks is close enough to capture dynamics in ABA. This yields the desired tractable fragment. We furthermore discuss consequences for the corresponding problems for logic programs.

We study the computational complexity of abstract argumentation semantics based on  weak admissibility, a recently introduced concept to deal with arguments of self-defeating  nature. Our results reveal that semantics based on weak admissibility are of much higher  complexity (under typical assumptions) compared to all argumentation semantics which  have been analysed in terms of complexity so far. In fact, we show PSPACE-completeness  of all non-trivial standard decision problems for weak-admissible based semantics. We then  investigate potential tractable fragments and show that restricting the frameworks under  consideration to certain graph-classes significantly reduces the complexity. We also show  that weak-admissibility based extensions can be computed by dividing the given graph into  its strongly connected components (SCCs). This technique ensures that the bottleneck  when computing extensions is the size of the largest SCC instead of the size of the graph  itself and therefore contributes to the search for fixed-parameter tractable implementations  for reasoning with weak admissibility. 

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.

We address the issue of quantitatively assessing the severity of inconsistencies in nonmonotonic frameworks. While measuring inconsistency in classical logics has been investigated for some time now, taking the nonmonotonicity into account poses new challenges. In order to tackle them, we focus on the structure of minimal strongly kb-inconsistent subsets of a knowledge base kb---a generalization of minimal inconsistency to arbitrary, possibly nonmonotonic, frameworks. We propose measures based on this notion and investigate their behavior in a nonmonotonic setting by revisiting existing rationality postulates, analyzing the compliance of the proposed measures with these postulates, and by investigating their computational complexity.

We present an approach to reasoning with strict and defeasible rules over literals. A controlled natural language is employed as human/machine interface to facilitate the specification of knowledge and verbalization of results. Reasoning on the rules is done by a direct semantics that addresses several issues for current approaches to argumentation-based defeasible reasoning. Techniques from formal argumentation theory are employed to justify conclusions of the approach; therefore, we not only address automated reasoning but also human acceptance of provided conclusions.

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.

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.

We analyze the relative expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued interpretations over a given propositional vocabulary A using only atoms from A. While the computational complexity of the two-valued model existence problem for all these languages is (almost) the same, we show that the languages form a neat hierarchy with respect to their expressiveness. We then demonstrate that this hierarchy collapses once we allow to introduce a linear number of new vocabulary elements.

We present various new concepts and results related to abstract dialectical frameworks (ADFs), a powerful generalization of Dung's argumentation frameworks (AFs). In particular, we show how the existing definitions of stable and preferred semantics which are restricted to the subcase of so-called bipolar ADFs can be improved and generalized to arbitrary frameworks. Furthermore, we introduce preference handling methods for ADFs, allowing for both reasoning with and about preferences. Finally, we present an implementation based on an encoding in answer set programming.