On local domain symmetry for model expansion

Devriendt, Jo; Bogaerts, Bart; Bruynooghe, Maurice; Denecker, Marc

doi:10.1017/s1471068416000508

Cited by 14 publications

(9 citation statements)

References 13 publications

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“…To overcome this, an understanding of a good initial abstraction needs to be investigated. Employing symmetry breaking techniques [34,37] in order to get hints on a good initial abstraction is a promising subject of future research. Furthermore, as the use of abstraction depends on the problem structure at hand, characterizations of different problem types and a better understanding of the effects of abstraction are necessary.…”

Section: Discussionmentioning

confidence: 99%

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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Section: Discussionmentioning

confidence: 99%

Abstraction for Non-ground Answer Set Programs

Saribatur

Schüller

Eiter

2019

Logics in Artificial Intelligence

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“…Symmetries can be detected and broken on the propositional level [Aloul et al 2006, Devriendt et al 2016b], but for large problems, even the task of detecting symmetries becomes infeasible. Detecting symmetries on the first-order theory [Devriendt et al 2016a] is often an easier problem, as much more structure of the problem is explicitly available. For example for an FO specification of the pigeonhole problem, it is almost trivial to detect that all pigeons are interchangeable.…”

Section: Preprocessingmentioning

confidence: 99%

“…For example for an FO specification of the pigeonhole problem, it is almost trivial to detect that all pigeons are interchangeable. The symmetry detection inference in IDP detects a simple, frequently occurring form of symmetries: locally interchangeable domain elements (see [Devriendt et al 2016a]). Two domain elements are considered interchangeable if they are of the same type and occur only symmetrically in interpreted predicates.…”

Section: Preprocessingmentioning

confidence: 99%

Predicate logic as a modeling language: the IDP system

Cat¹,

Bogaerts

Bruynooghe³

et al. 2018

Declarative Logic Programming: Theory, Systems, and Applications

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With the technology of the time, Kowalski's seminal 1974 paper Predicate Logic as a Programming Language was a breakthrough for the use of logic in computer science. It introduced two fundamental ideas: on the declarative side, the use of the Horn clause logic fragment of classical logic, which was soon extended with negation as failure, on the procedural side the procedural interpretation which made it possible to write algorithms in the formalism.Since then, strong progress was made both on the declarative understanding of the logic programming formalism and in automated reasoning technologies, particularly in SAT solving, Constraint Programming and Answer Set Programming. This has paved the way for the development of an extension of logic programming that embodies a more pure view of logic as a modelling language and its role for problem solving.In this chapter, we present the IDP language and system. The language is essentially classical logic extended with one of logic programmings most important contributions to knowledge representation: the representation of complex definitions as rule sets under wellfounded semantics. The system is a knowledge base system: a system in which complex declarative information is stored in a knowledge base which can be used to solve different computational problems by applying multiple forms of inference. In this view, theories are declarative modellings, bags of information, i.e., descriptions of possible states of affairs. They are neither procedures nor descriptions of computational problems. As such, the IDP language and system preserve the fundamental idea of a declarative reading of logic programs, while they break with the fundamental idea of the procedural interpretation of logic programs.

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“…The model-based methods are usually applied offline and aim at finding general SBCs breaking symmetries of a class of instances. However, these methods are either limited to local symmetries occurring due to definitions of variable domains (Devriendt et al 2016) or require representative sets of instances (Mears et al 2008;Tarzariol et al 2021) to identify SBCs that highly likely eliminate symmetries for all instances of this class. Roughly, model-based approaches apply graphbased methods, for example, saucy (Darga et al 2004), to find candidate symmetries of the given instances and then lift the obtained information to first-order SBCs.…”

Section: Introductionmentioning

confidence: 99%

Efficient Lifting of Symmetry Breaking Constraints for Complex Combinatorial Problems

Tarzariol

Schekotihin²,

Gebser³

et al. 2022

Theory and Practice of Logic Programming

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Many industrial applications require finding solutions to challenging combinatorial problems. Efficient elimination of symmetric solution candidates is one of the key enablers for high-performance solving. However, existing model-based approaches for symmetry breaking are limited to problems for which a set of representative and easily solvable instances is available, which is often not the case in practical applications. This work extends the learning framework and implementation of a model-based approach for Answer Set Programming to overcome these limitations and address challenging problems, such as the Partner Units Problem. In particular, we incorporate a new conflict analysis algorithm in the Inductive Logic Programming system ILASP, redefine the learning task, and suggest a new example generation method to scale up the approach. The experiments conducted for different kinds of Partner Units Problem instances demonstrate the applicability of our approach and the computational benefits due to the first-order constraints learned.

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On local domain symmetry for model expansion

Cited by 14 publications

References 13 publications

Abstraction for Non-ground Answer Set Programs

Abstraction for Non-ground Answer Set Programs

Predicate logic as a modeling language: the IDP system

Efficient Lifting of Symmetry Breaking Constraints for Complex Combinatorial Problems

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