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. 

In this solver description we present ASPARTIX-V, in its 2021 edition, which participates in the International Competition on Computational Models of Argumentation (ICCMA) 2021. ASPARTIX-V is capable of solving all classical (static) reasoning tasks part of ICCMA'21 and extends the ASPARTIX system suite by incorporation of recent ASP language constructs (e.g. conditional literals), domain heuristics within ASP, and multi-shot methods. In this light ASPARTIX-V deviates from the traditional focus of ASPARTIX on monolithic approaches (i.e., one-shot solving via a single ASP encoding) to further enhance performance.

Generalizing the attack structure in argumentation frameworks (AFs) has been studied in different ways. Most prominently, the binary attack relation of Dung frameworks has been extended to the notion of collective attacks. The resulting formalism is often termed SETAFs. Another approach is provided via abstract dialectical frameworks (ADFs), where acceptance conditions specify the relation between arguments; restricting these conditions naturally allows for so-called support-free ADFs. The aim of the paper is to shed light on the relation between these two different approaches. To this end, we investigate and compare the expressiveness of SETAFs and support-free ADFs under the lens of 3-valued semantics. Our results show that it is only the presence of unsatisfiable acceptance conditions in support-free ADFs that discriminate the two approaches.

We consider planning problems for graphs, Markov decision processes (MDPs), and games on graphs. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an adversarial environment.We consider two planning problems where there are k different target sets, and the problems are as follows: (a) the coverage problem asks whether there is a plan for each individual target set, and (b) the sequential target reachability problem asks whether the targets can be reached in sequence. For the coverage problem, we present a linear-time algorithm for graphs, and quadratic conditional lower bound for MDPs and games on graphs.For the sequential target problem, we present a linear-time algorithm for graphs, a sub-quadratic algorithm for MDPs, and a quadratic conditional lower bound for games on graphs.Our results with conditional lower bounds establish (i) model-separation results showing that for the coverage problem MDPs and games on graphs are harder than graphs and for the sequential reachability problem games on graphs are harder than MDPs and graphs;and (ii) objective-separation results showing that for MDPs the coverage problem is harder than the sequential target problem.

We consider planning problems for graphs, Markov decision processes (MDPs), and games on graphs. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an adversarial environment. We consider two planning problems where there are k different target sets, and the problems are as follows: (a) the coverage problem asks whether there is a plan for each individual target set, and (b) the sequential target reachability problem asks whether the targets can be reached in sequence. For the coverage problem, we present a linear-time algorithm for graphs and quadratic conditional lower bound for MDPs and games on graphs. For the sequential target problem, we present a linear-time algorithm for graphs, a sub-quadratic algorithm for MDPs, and a quadratic conditional lower bound for games on graphs. Our results with conditional lower bounds establish (i) model-separation results showing that for the coverage problem MDPs and games on graphs are harder than graphs and for the sequential reachability problem games on graphs are harder than MDPs and graphs; (ii) objective-separation results showing that for MDPs the coverage problem is harder than the sequential target problem.

The aim of this paper is to announce the release of a novel system for abstract argumentation which is based on decomposition and dynamic programming. We provide first experimental evaluations to show the feasibility of this approach.

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 frontend for the ASP-package gringo/claspD provides 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.