Smodels A — A System for Computing Answer Sets of Logic Programs with Aggregates

Elkabani, Islam; Pontelli, Enrico; Son, Tran Cao

doi:10.1007/11546207_40

Cited by 20 publications

(12 citation statements)

References 1 publication

(1 reference statement)

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“…Moreover, ASP solvers-see e.g. Alviano et al 2013;Elkabani et al 2005;Alviano et al 2010)-have made huge strides in efficiency. A logic program usually consists of a set of logical implications (called rules) and a set of facts.…”

Section: Introductionmentioning

confidence: 99%

The power of non-ground rules in Answer Set Programming

Bichler¹,

Morak²,

Woltran³

2016

Theory and Practice of Logic Programming

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Answer set programming (ASP) is a well-established logic programming language that offers an intuitive, declarative syntax for problem solving. In its traditional application, a fixed ASP program for a given problem is designed and the actual instance of the problem is fed into the program as a set of facts This approach typically results in programs with comparably short and simple rules However, as is known from complexity analysis, such an approach limits the expressive power of ASP; in fact, an entire NP-check can be encoded into a single large rule body of bounded arity that performs both a guess and a check within the same rule Here, we propose a novel paradigm for encoding hard problems in ASP by making explicit use of large rules which depend on the actual instance of the problem. We illustrate how this new encoding paradigm can be used, providing examples of problems from the first, second, and even third level of the polynomial hierarchy As state-of-the-art solvers are tuned towards short rules, rule decomposition is a key technique in the practical realization of our approach We also provide some preliminary benchmarks which indicate that giving up the convenient way of specifying a fixed program can lead to a significant speed-up. This paper is under consideration for acceptance in TPLP.

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Section: Introductionmentioning

confidence: 99%

The power of non-ground rules in Answer Set Programming

Bichler¹,

Morak²,

Woltran³

2016

Theory and Practice of Logic Programming

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“…We refer to logic programs with these constraints as weight constraint, aggregate, and abstract constraint programs, respectively. Much research has been done on the application and implementations of weight constraint and aggregate programs [3,8,11,14,18,26].…”

Section: Introductionmentioning

confidence: 99%

Level Mapping Induced Loop Formulas for Weight Constraint and Aggregate Logic Programs

You

2010

Fundamenta Informaticae

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Level mapping and loop formulas are two different means to justify and characterize answer sets for normal logic programs. Both of them specify conditions under which a supported model is an answer set. Though serving a similar purpose, in the past the two have been studied largely in isolation with each other. In this paper, we study level mapping and loop formulas for weight constraint and aggregate (logic) programs. We show that, for these classes of programs, loop formulas can be devised from level mapping characterizations. First, we formulate a level mapping characterization of stable models and show that it leads to a new formulation of loop formulas for arbitrary weight constraint programs, without using any new atoms. This extends a previous result on loop formulas for weight constraint programs, where weight constraints contain only positive literals. Second, since aggregate programs are closely related to weight constraint programs, we further use level mapping to characterize the underlying answer set semantics based on which we formulate loop formulas for aggregate programs. The main result is that for aggregate programs not involving the inequality comparison operator, the dependency graphs can be built in polynomial time. This compares to the previously known exponential time method.

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“…A large number of extended modeling languages have also been previously proposed. On one hand, ASP languages have been extended with constraints or other externally defined relations (see, e.g., [6][7][8][9][10][11]). On the other hand, Prolog systems have been extended with ASP features [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

A Module-Based Framework for Multi-language Constraint Modeling

Järvisalo¹,

Oikarinen²,

Janhunen³

et al. 2009

Logic Programming and Nonmonotonic Reasoning

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Abstract. We develop a module-based framework for constraint modeling where it is possible to combine different constraint modeling languages and exploit their strengths in a flexible way. In the framework a constraint model consists of modules with clear input/output interfaces. When combining modules, apart from the interface, a module is a black box whose internals are invisible to the outside world. Inside a module a chosen constraint language (approaches such as CP, ASP, SAT, and MIP) can be used. This leads to a clear modular semantics where the overall semantics of the whole constraint model is obtained from the semantics of individual modules. The framework supports multi-language modeling without the need to develop a complicated joint semantics and enables the use of alternative semantical underpinnings such as default negation and classical negation in the same model. Furthermore, computational aspects of the framework are considered and, in particular, possibilities of benefiting from the known module structure in solving constraint models are studied.

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Smodels A — A System for Computing Answer Sets of Logic Programs with Aggregates

Cited by 20 publications

References 1 publication

The power of non-ground rules in Answer Set Programming

The power of non-ground rules in Answer Set Programming

Level Mapping Induced Loop Formulas for Weight Constraint and Aggregate Logic Programs

A Module-Based Framework for Multi-language Constraint Modeling

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