Cautious reasoning in ASP via minimal models and unsatisfiable cores

Alviano, Mario; Dodaro, Carmine; Järvisalo, Matti; Maratea, Marco; Previti, Alessandro

doi:10.1017/s1471068418000145

Cited by 8 publications

(22 citation statements)

References 42 publications

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“…Moreover, given a logic program Π, we say that a set C ⊆ lit(atoms(Π)) is a core of Π, if Π ∪ {← l|l ∈ C} is incoherent. It is important to emphasize here that this definition is in line with the one proposed by Alviano et al (2018). In particular, unsatisfiable cores have two important properties:…”

Section: Core-based Methodssupporting

confidence: 55%

“…Such advanced techniques have been borrowed from the computation of backbones of propositional formulas. We have then designed new solving procedures, and implemented them in WASP, that already included algorithms of (Alviano et al 2014;Alviano et al 2018). Experiments on devoted benchmarks have shown positive results for the new proposed solutions.…”

Section: Resultsmentioning

confidence: 99%

“…• an atom p ∈ atoms(Π) is a cautious consequence of Π if and only if {¬p} is an unsatisfiable core (Proposition 4.1 of (Alviano et al 2018)).…”

Section: Core-based Methodsmentioning

confidence: 99%

“…• if C is an unsatisfiable core of Π then all of its supersets are also unsatisfiable cores of Π; • an atom p ∈ atoms(Π) is a cautious consequence of Π if and only if {¬p} is an unsatisfiable core (Proposition 4.1 of (Alviano et al 2018)).…”

Section: Core-based Methodsmentioning

confidence: 99%

“…As a reference to the state of the art, we used CLASP v. 3.3.3 (Gebser et al 2012), which implements algorithm OR (i.e., over-approximation), and the best performing algorithms implemented by WASP (Alviano et al 2014;Alviano et al 2018), namely OR (i.e., over-approximation), ICT (i.e., under-approximation), OPT, and CM. Algorithm OPT was presented in (Alviano et al 2018). The idea is as follows.…”

Section: Experimental Analysismentioning

confidence: 99%

See 4 more Smart Citations

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: Core-based Methodssupporting

confidence: 55%

Section: Resultsmentioning

confidence: 99%

“…• an atom p ∈ atoms(Π) is a cautious consequence of Π if and only if {¬p} is an unsatisfiable core (Proposition 4.1 of (Alviano et al 2018)).…”

Section: Core-based Methodsmentioning

confidence: 99%

Section: Core-based Methodsmentioning

confidence: 99%

Section: Experimental Analysismentioning

confidence: 99%

See 3 more Smart Citations

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

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Abstraction for Non-ground Answer Set Programs

Saribatur

Schüller

Eiter

2019

Logics in Artificial Intelligence

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ion is an important technique utilized by humans in model building and problem solving, in order to figure out key elements and relevant details of a world of interest. This naturally has led to investigations of using abstraction in AI and Computer Science to simplify problems, especially in the design of intelligent agents and automated problem solving. By omitting details, scenarios are reduced to ones that are easier to deal with and to understand, where further details are added back only when they matter. Despite the fact that abstraction is a powerful technique, it has not been considered much in the context of nonmonotonic knowledge representation and reasoning, and specifically not in Answer Set Programming (ASP), apart from some related simplification methods. In this work, we introduce a notion for abstracting from the domain of an ASP program such that the domain size shrinks while the set of answer sets (i.e., models) of the program is over-approximated. To achieve the latter, the program is transformed into an abstract program over the abstract domain while preserving the structure of the rules. We show in elaboration how this can be also achieved for single or multiple sub-domains (sorts) of a domain, and in case of structured domains like grid environments in which structure should be preserved. Furthermore, we introduce an abstraction-&-refinement methodology that makes it possible to start with an initial abstraction and to achieve automatically an abstraction with an associated abstract answer set that matches an answer set of the original program, provided that the program is satisfiable. Experiments based on prototypical implementations reveal the potential of the approach for problem analysis, by its ability to focus on the parts of the program that cause unsatisfiability and by achieving concrete abstract answer sets that merely reflect relevant details. This makes domain abstraction an interesting topic of research whose further use in important areas like Explainable AI remains to be explored.

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