Answer Set Programming Modulo Acyclicity*

Bomanson, Jori; Gebser, Martin; Janhunen, Tomi; Kaufmann, Benjamin; Schaub, Torsten

doi:10.3233/fi-2016-1398

Cited by 29 publications

(39 citation statements)

References 30 publications

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“…A program P is called tight, if loop(P) = / 0. While we allow programs with loops that might also involve atoms of weight rules, we consider weight rules only as a compact representation of a set of normal rules, similar to the definition of stable models in related work (Bomanson et al 2016). In other words, we do not consider advanced semantics concerning recursive weight rules (recursive aggregates).…”

Section: Answer Set Programming (Asp)mentioning

confidence: 99%

Inconsistency Proofs for ASP: The ASP - DRUPE Format

Alviano

Dodaro

Fichte

et al. 2019

Theory and Practice of Logic Programming

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Answer Set Programming (ASP) solvers are highly-tuned and complex procedures that implicitly solve the consistency problem, i.e., deciding whether a logic program admits an answer set. Verifying whether a claimed answer set is formally a correct answer set of the program can be decided in polynomial time for (normal) programs. However, it is far from immediate to verify whether a program that is claimed to be inconsistent, indeed does not admit any answer sets. In this paper, we address this problem and develop the new proof format ASP-DRUPE for propositional, disjunctive logic programs, including weight and choice rules. ASP-DRUPE is based on the Reverse Unit Propagation (RUP) format designed for Boolean satisfiability. We establish correctness of ASP-DRUPE and discuss how to integrate it into modern ASP solvers. Later, we provide an implementation of ASP-DRUPE into the wasp solver for normal logic programs.

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Section: Answer Set Programming (Asp)mentioning

confidence: 99%

Inconsistency Proofs for ASP: The ASP - DRUPE Format

Alviano

Dodaro

Fichte

et al. 2019

Theory and Practice of Logic Programming

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“…There are also theory-based extensions of ASP and the general framework has shaped up in a number of works, see [19] for a summary of existing approaches and tools. One notable theory concerns graph properties in analogy to SMG and, in particular, that of acyclicity [4]. Although many graph properties including acyclicity are expressible in ASP itself, it may be desirable to use graph-based extensions for the sake of compact representation or more efficient, explicit reasoning based on graphs.…”

Section: Sat Modulo Theoriesmentioning

confidence: 99%

“…Although many graph properties including acyclicity are expressible in ASP itself, it may be desirable to use graph-based extensions for the sake of compact representation or more efficient, explicit reasoning based on graphs. Moreover, acyclicity is so frequently occurring property in applications that a dedicated implementation, such as the one devised in [4], is justifiable.…”

Section: Sat Modulo Theoriesmentioning

confidence: 99%

Answer Set Programming

Janhunen

2018

Künstl Intell

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Answer set programming (ASP) is a declarative programming paradigm based on an interpretation of logical rules as constraints. In this article, we relate answer set programming with other constraint-based solving paradigms: Boolean satisfiability checking, satisfiability modulo theories, mixed integer programming, and constraint programming. We illustrate the relationship of ASP with these alternative paradigms in terms of simple examples, and identify the main primitives and characteristics of the constraintbased languages under consideration.

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“…Any subset of these pairs can be generated via the choice rule in line 4, permitting instances of edge/2 to hold without further preconditions. 1 For example, the atoms characterizing the directed graph in Figure 1(a) are edge (1,2), edge (1,3), edge (2,4), edge (3,2), edge (4,5), and edge (5,3).…”

Section: Directed Acyclic Graphsmentioning

confidence: 99%

“…Acyclicity Checking To make sure that a generated directed graph V, E is acyclic, we may check whether there is a strict partial order < over vertices in V such that u < v if u, v ∈ E. The rules in Figure 3 encode this approach in an inductive fashion, where atoms of the form order(u,v) indicate the absence of cycles involving an edge candidate u, v and order(u) expresses the same for vertices u. Given n=5, the following (simplified) ground instances are obtained when the label 3 is substituted for X: order(3,1) :-not edge (3,1). order(3,1) :-order(1).…”

Section: Directed Acyclic Graphsmentioning

confidence: 99%

Declarative encodings of acyclicity properties

Gebser

Janhunen

Rintanen

2015

Journal of Logic and Computation

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Many knowledge representation tasks involve trees or similar structures as abstract datatypes. However, devising compact and efficient declarative representations of such structural properties is non-obvious and can be challenging indeed. In this article, we take a number of acyclicity properties into consideration and investigate various logic-based approaches to encode them. We use answer set programming as the primary representation language but also consider mappings to related formalisms, such as propositional logic, difference logic and linear programming. We study the compactness of encodings and the resulting computational performance on benchmarks involving acyclic or tree structures.

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Answer Set Programming Modulo Acyclicity*

Cited by 29 publications

References 30 publications

Inconsistency Proofs for ASP: The ASP - DRUPE Format

Inconsistency Proofs for ASP: The ASP - DRUPE Format

Answer Set Programming

Declarative encodings of acyclicity properties

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