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.

The state of each component is determined by a Boolean function of the state of (a subset of) the components of the network. This paper addresses the synthesis of these Boolean functions from constraints on their domain and emerging dynamical properties of the resulting network. The dynamical properties relate to the existence and absence of trajectories between partially observed configurations, and to the stable behaviours (fixpoints and cyclic attractors). The synthesis is expressed as a Boolean satisfiability problem relying on Answer-Set Programming with a parametrized complexity, and leads to a complete non-redundant characterization of the set of solutions. Considered constraints are particularly suited to address the synthesis of models of cellular differentiation processes, as illustrated on a case study. The scalability of the approach is demonstrated on random networks with scale-free structures up to 100 to 1,000 nodes depending on the type of constraints.

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.

Update semantics for Answer-Set Programming assign models to sequences of answer-set programs which result from the iterative process of updating programs by programs. Each program in the sequence represents an update of the preceding ones. One of the enduring problems in this context is state condensing, or the problem of determining a single logic program that faithfully represents the sequence of programs. Such logic program should 1) be written in the same alphabet, 2) have the same stable models, and 3) be equivalent to the sequence of programs when subject to further updates. It has been known for more than a decade that update semantics easily lead to non-minimal stable models, so an update sequence cannot be represented by a single non-disjunctive program. On the other hand, more expressive classes of programs were never considered, mainly because it was not clear how they could be updated further. In this paper we solve the state condensing problem for two foundational rule update semantics, using nested logic programs. Furthermore, we also show that disjunctive programs with default negation in the head can be used for the same purpose.

The practical results of answer-set programming indicate that classical complexity theory is insufficient as a theoretical framework to explain why modern answer-set programming solvers work fast on industrial applications. Complexity analysis by means of parameterized complexity theory seems to be promising, because we think that the reason for the gap between theory and practice is the presence of a "hidden structure" in real-world instances. The application of parameterized complexity theory to answer-set programming would give a crucial understanding of how solver heuristics work. This profound understanding can be used to improve the decision heuristics of modern solvers and yields new efficient algorithms for decision problems in the nonmonotonic setting. My research aims to explain the gap between theoretical upper bounds and the effort to solve real-world instances. I will further develop by means of parameterized complexity exact algorithms which work efficiently for real-world instances. The approach is based on backdoors which are small sets of atoms that represent "clever reasoning shortcuts" through the search space. The concept of backdoors is widely used in the areas of propositional satisfiability and constraint satisfaction. I will show how this concept can be adapted to the nonmonotonic setting and how it can be utilized to improve common algorithms.

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.

In this paper, we present a novel approach to the evaluation of propositional answer-set programs. In particular, for programs with bounded treewidth, our algorithm is capable of (i) computing the number of answer sets in linear time and (ii) enumerating all answer sets with linear delay. Our algorithm relies on dynamic programming, which so far has not been applied to ASP-problems. Therefore, our approach significantly differs from standard ASP-systems which implement techniques stemming from SAT or CSP, and thus usually do not exploit fixed parameter properties of the programs. We provide first experimental results which underline that, for programs with low treewidth, already a prototypical implementation is competitive compared to state-of-the-art systems.