Abstract Solvers for Dung’s Argumentation Frameworks

Brochenin, Rémi; Linsbichler, Thomas; Maratea, Marco; Wallner, Johannes; Woltran, Stefan

doi:10.1007/978-3-319-28460-6_3

Cited by 6 publications

(4 citation statements)

References 16 publications

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“…As far as the application of abstract solvers methodology outside ASP is concerned, the first application has been already mentioned and is related to the seminal paper (Nieuwenhuis et al 2006), where SMT problems with certain logics via a lazy approach (Sebastiani 2007) are considered. Then, abstract solvers have been presented for the satisfiability of Quantified Boolean Formulas by Brochenin and Maratea (2015b), and for solving certain reasoning taks in Abstract Argumentation under preferred semantics (Brochenin et al 2018). Finally, in another number of papers, starting from a developed concept of modularity in answer set solving (Lierler and Truszczynski 2013), abstract modeling of solvers for multi-logic systems are presented (Lierler and Truszczynski 2014;Lierler and Truszczynski 2015;Lierler and Truszczynski 2016).…”

Section: Related Workmentioning

confidence: 99%

“…Another added, general, value of our paper is in its practical part, i.e., an implementation of new solutions designed through abstract solvers. In fact, while nowadays abstract solvers methodology has been widely used, often in the mentioned papers the presented results have rarely led to implementations, with the exception of (Nieuwenhuis et al 2006), where the related BARCE-LOGIC implementation won the SMT Competition 2005 on same logics, and (Lierler 2011), where a proposed combination of SMODELS and CMODELS techniques has been implemented in the solver SUP, that reached positive results at the ASP Competition 2011 and, more recently, (Brochenin et al 2018), where the new designed solution, obtained as a modification of the CEGARTIX solver, performed often better than the basic CERGATIX solver on preferred semantics, that was among the best solvers in the first ICCMA competition.…”

Section: Related Workmentioning

confidence: 99%

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Abstract Solvers for Computing Cautious Consequences of ASP programs

Amendola¹,

Dodaro²,

Maratea³

2019

Theory and Practice of Logic Programming

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solvers are a method to formally analyze algorithms that have been profitably used for describing, comparing and composing solving techniques in various fields such as Propositional Satisfiability (SAT), Quantified SAT, Satisfiability Modulo Theories, Answer Set Programming (ASP), and Constraint ASP.In this paper, we design, implement and test novel abstract solutions for cautious reasoning tasks in ASP. We show how to improve the current abstract solvers for cautious reasoning in ASP with new techniques borrowed from backbone computation in SAT, in order to design new solving algorithms. By doing so, we also formally show that the algorithms for solving cautious reasoning tasks in ASP are strongly related to those for computing backbones of Boolean formulas. We implement some of the new solutions in the ASP solver WASP and show that their performance are comparable to state-of-the-art solutions on the benchmark problems from the past ASP Competitions. Under consideration for acceptance in TPLP. KEYWORDS:Answer Set Programming, Abstract solvers, Cautious reasoning solver, SUP (Lierler 2011); however, abstract solvers have been so far mainly applied to ASP solvers for brave reasoning tasks where, given an input query and a knowledge base expressed in ASP, answers are witnessed by ASP solutions, i.e., stable models (Baral 2003;Eiter et al. 1997;Gelfond and Lifschitz 1988;Gelfond and Lifschitz 1991;Marek and Truszczyński 1998;Niemelä 1999).However, in ASP, also cautious reasoning has been deeply studied in the literature: answers here must be witnessed by all stable models. This task has found a significant number of interesting applications as well, including consistent query answering (Arenas et al. 2003;Manna et al. 2013), data integration (Eiter 2005), multi-context systems (Brewka and Eiter 2007), and ontology-based reasoning (Eiter et al. 2008). Two well-known ASP solvers, i.e., DLV (Leone et al. 2006) and CLASP (Gebser et al. 2012), have been extended for computing cautious consequences of ASP programs. More recently, Alviano et al. (2014) presented a unified, high-level view of such solving procedures, and designed several algorithms for cautious reasoning in ASP, including those implemented in DLV and CLASP, borrowed from the backbone computation of Boolean formulas (Janota et al. 2015): all these techniques are implemented (and tested) on top of the ASP solver WASP (Alviano et al. 2015).In this paper we design, implement and test novel abstract solutions for cautious reasoning tasks in ASP. We show how to improve the current abstract solvers (Brochenin and Maratea 2015a) for cautious reasoning in ASP with further techniques borrowed from backbone computation in SAT, in order to design new solving algorithms. In particular, we import a technique called "chunk", which generalizes over-and under-approximation by testing a set soft atoms simultaneously for being added in the under-approximation, and core-based algorithms, which can be considered either a solution per se, or a way for pruning the set of atoms t...

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Abstract Solvers for Computing Cautious Consequences of ASP programs

Amendola¹,

Dodaro²,

Maratea³

2019

Theory and Practice of Logic Programming

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this analysis we compare prefASP and prefMaxSAT with the winner of the the IC-CMA2015 track on enumerating preferred extensions, Cegartix [8]. Table 4 shows the performance of considered solvers in terms of IPC score, percentage of successfully analysed AF s and PAR10.…”

Section: Comparison With the State Of The Art Solvermentioning

confidence: 99%

Solving Set Optimization Problems by Cardinality Optimization via Weak Constraints with an Application to Argumentation

Faber,

Vallati,

Cerutti

et al. 2016

Preprint

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Optimization-minimization or maximization-in the lattice of subsets is a frequent operation in Artificial Intelligence tasks. Examples are subsetminimal model-based diagnosis, nonmonotonic reasoning by means of circumscription, or preferred extensions in abstract argumentation. Finding the optimum among many admissible solutions is often harder than finding admissible solutions with respect to both computational complexity and methodology. This paper addresses the former issue by means of an effective method for finding subsetoptimal solutions. It is based on the relationship between cardinality-optimal and subset-optimal solutions, and the fact that many logic-based declarative programming systems provide constructs for finding cardinality-optimal solutions, for example maximum satisfiability (MaxSAT) or weak constraints in Answer Set Programming (ASP). Clearly each cardinality-optimal solution is also a subsetoptimal one, and if the language also allows for the addition of particular restricting constructs (both MaxSAT and ASP do) then all subset-optimal solutions can be found by an iterative computation of cardinality-optimal solutions. As a showcase, the computation of preferred extensions of abstract argumentation frameworks using the proposed method is studied.

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“…The current paper extends and differs from an earlier version [8] as follows: (i) a new combination of abstract solvers is presented, which is easier to understand and more amenable to be implemented than…”

Section: Introductionmentioning

confidence: 99%

Abstract solvers for Dung’s argumentation frameworks

Brochenin

Linsbichler

Maratea

et al. 2018

AAC

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TU Wien, Austria E-mails: linsbich@dbai.tuwien.ac.at, wallner@dbai.tuwien.ac.at, woltran@dbai.tuwien.ac.at Abstract. Abstract solvers are a quite recent method to uniformly describe algorithms in a rigorous formal way via graphs. Compared to traditional methods like pseudo-code descriptions, abstract solvers have several advantages. In particular, they provide a uniform formal representation that allows for precise comparisons of different algorithms. Recently, this new methodology has proven successful in declarative paradigms such as Propositional Satisfiability and Answer Set Programming. In this paper, we apply this machinery to Dung's abstract argumentation frameworks. We first provide descriptions of several advanced algorithms for the preferred semantics in terms of abstract solvers. We also show how it is possible to obtain new abstract solutions by "combining" concepts of existing algorithms by means of combining abstract solvers. Then, we implemented a new solving procedure based on our findings in CEGARTIX, and call it CEGARTIX+. We finally show that CEGARTIX+ is competitive and complementary in its performance to CEGARTIX on benchmarks of the first and second argumentation competition.Keywords: Abstract argumentation, abstract solvers IntroductionDung's concept of abstract argumentation [23] is nowadays a core formalism in Artificial Intelligence [4,46]. The problem of solving certain reasoning tasks on such frameworks is the centerpiece of many advanced higher-level argumentation systems. The problems to be solved can however be intractable and might even be hard for the second level of the polynomial hierarchy [24,26]. Thus, efficient and advanced algorithms have to be developed in order to deal with real-world size data within reasonable performance bounds. The argumentation community is currently facing this challenge [17] [44]. Hereby, one characterizes the possible states of computation as nodes of a graph, and the techniques (i.e., the computation steps in the algorithms) as arcs between nodes. In this way, the whole solving process amounts to a path in the graph. This concept proved successful for SAT [44], and also has been applied to several variants of Answer Set Programming [6,36,37].In this paper, we apply abstract solvers to certain problems in Dung's argumentation frameworks. In order to understand whether abstract solvers are well suited also for this domain, we consider quite advanced algorithms for solving problems that are hard for the second level of the polynomial hierarchy -the considered algorithms range from dedicated [45] to reduction-based [13,25] approaches (see [19] for a survey). We show that abstract solvers allow for convenient algorithms design resulting in a clear and mathematically precise description. Moreover, formal properties of the algorithms (i.e. correctness) are easily specified by means of related graph properties (i.e. reachability). We then illustrate how abstract solvers allow to highlight in a more clear way similarities and differences among solvin...

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Abstract Solvers for Dung’s Argumentation Frameworks

Cited by 6 publications

References 16 publications

Abstract Solvers for Computing Cautious Consequences of ASP programs

Abstract Solvers for Computing Cautious Consequences of ASP programs

Solving Set Optimization Problems by Cardinality Optimization via Weak Constraints with an Application to Argumentation

Abstract solvers for Dung’s argumentation frameworks

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