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Unsatisfiable Core Analysis and Aggregates for Optimum Stable Model Search

Alviano Mario, Dodaro Carmine

Fundamenta Informaticae

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2020

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Vol. 176, nr 3/4

271--297

EN

Many efficient algorithms for the computation of optimum stable models in the context of Answer Set Programming (ASP) are based on unsatisfiable core analysis. Among them, algorithm OLL was the first introduced in the context of ASP, whereas algorithms ONE and PMRES were first introduced for solving the Maximum Satisfiability problem (MaxSAT) and later on adapted to ASP. In this paper, we present the porting to ASP of another state-of-the-art algorithm introduced for MaxSAT, namely K, which generalizes ONE and PMRES. Moreover, we present a new algorithm called OLL-IN-ONE that compactly encodes all aggregates of OLL by taking advantage of shared aggregate sets propagators. The performance of the algorithms have been empirically compared on instances taken from the latest ASP Competition.

2

Model Enumeration via Assumption Literals

Alviano Mario, Dodaro Carmine

Fundamenta Informaticae

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2019

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Vol. 167, nr 1-2

31--58

EN

Modern, efficient Answer Set Programming solvers implement answer set search via non-chronological backtracking algorithms. The extension of these algorithms to answer set enumeration is nontrivial. In fact, adding blocking constraints to discard already computed answer sets is inadequate because the introduced constraints may not fit in memory or deteriorate the efficiency of the solver. On the other hand, the algorithm implemented by CLASP, which can run in polynomial space, requires to modify the answer set search procedure. The algorithm is revised in this paper so as to make it almost independent from the underlying answer set search procedure, provided that the procedure accepts as input a logic program and a list of assumption literals, and returns an answer set (and associated branching literals). In fact, thanks to an alternative view in terms of transition systems, the revised algorithm is suitable to easily accommodate the enumerate of models of other Boolean languages, among them classical models of propositional theories. On a pragmatic level, the paper presents two implementations of the enumeration algorithm, in WASP for answer set enumeration, and in GLUCOSE for classical models enumeration. The implemented systems are compared empirically to the state of the art solver CLASP.

3

Argumentation Reasoning via Circumscription with Pyglaf

Alviano Mario

Fundamenta Informaticae

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2019

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Vol. 167, nr 1-2

1--30

EN

The fundamental mechanism that humans use in argumentation can be formalized in abstract argumentation frameworks. Many semantics are associated with abstract argumentation frameworks, each one consisting of a set of extensions, that is, a set of sets of arguments. Some of these semantics are based on preference relations that essentially impose to maximize or minimize some property. This paper presents the argumentation reasoner PYGLAF, which provides a uniform view of many semantics for abstract argumentation frameworks in terms of circumscription. Specifically, several computational problems of abstract argumentation frameworks are reduced to circumscription by means of linear encodings, and a few others are solved by means of a sequence of calls to an oracle for circumscription. Finally, grounded extensions are obtained in polynomial time by unit propagation, and acceptance problems are addressed by first checking cardinality optimal models of circumscribed theories, so that the naive extension enumeration is possibly avoided.