Abstract Modular Inference Systems and Solvers

Lierler, Yuliya; Truszczyński, Mirosław

doi:10.1007/978-3-319-04132-2_4

Cited by 10 publications

(11 citation statements)

References 15 publications

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“…(The recent clause tableaux proof system for MaxSAT [23] does not capture core-guided transformations or MaxSAT preprocessing, either.) The recent formalization of implicit hitting set (IHS) algorithms for optimization modulo theories of [13] captures solely extensions of the IHS approach [12,32], extending the DPLL(T) [31] which has also earlier been extended to optimization modulo theories [30] and adapted for formalizing answer set solvers [11,24] (without optimization statements).…”

Section: Related Workmentioning

confidence: 99%

Unifying Reasoning and Core-Guided Search for Maximum Satisfiability

Berg

Järvisalo

2019

Logics in Artificial Intelligence

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A central algorithmic paradigm in maximum satisfiability solving geared towards real-world optimization problems is the coreguided approach. Furthermore, recent progress on preprocessing techniques is bringing in additional reasoning techniques to MaxSAT solving. Towards realizing their combined potential, understanding formal underpinnings of interleavings of preprocessing-style reasoning and core-guided algorithms is important. It turns out that earlier proposed notions for establishing correctness of core-guided algorithms and preprocessing, respectively, are not enough for capturing correctness of interleavings of the techniques. We provide an in-depth analysis of these and related MaxSAT instance transformations, and propose correction set reducibility as a notion that captures inprocessing MaxSAT solving within a state-transition style abstract MaxSAT solving framework. Furthermore, we establish a general theorem of correctness for applications of SAT-based preprocessing techniques in MaxSAT. The results pave way for generic techniques for arguing about the formal correctness of MaxSAT algorithms.

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Section: Related Workmentioning

confidence: 99%

Unifying Reasoning and Core-Guided Search for Maximum Satisfiability

Berg

Järvisalo

2019

Logics in Artificial Intelligence

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“…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%

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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“…Other works on abstract solvers are [38], where solvers for different formalisms, e.g. ASP and SAT with Inductive Definitions, are compared by means of comparison of the related graphs, and the following series of papers where, starting from a developed concept of modularity in answer set solving [39], abstract modeling of solvers for multi-logic systems are presented [40][41][42].…”

Section: Related Workmentioning

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 Modular Inference Systems and Solvers

Cited by 10 publications

References 15 publications

Unifying Reasoning and Core-Guided Search for Maximum Satisfiability

Unifying Reasoning and Core-Guided Search for Maximum Satisfiability

Abstract Solvers for Computing Cautious Consequences of ASP programs

Abstract solvers for Dung’s argumentation frameworks

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