Two-Literal Logic Programs and Satisfiability Representation of Stable Models: A Comparison

Huang, Guan-Shieng; Jia, Xiumei; Liau, Churn‐Jung; You, Jia-Huai

doi:10.1007/3-540-47922-8_11

Cited by 5 publications

(8 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the problem becomes interesting when we drop the requirement of modularity. In the special case when all rules in a program have at most one literal in their bodies (so-called 2-literal programs), Huang et al [8] showed that there is an efficient translation to sets of clauses that do not need to use any extra variables. They also observed that many of the logic programs in answer set programming applications are essentially 2-literal ones.…”

Section: Introductionmentioning

confidence: 99%

ASSAT: computing answer sets of a logic program by SAT solvers

Lin

Zhao

2004

Artificial Intelligence

301

336

View full text Add to dashboard Cite

We propose a new translation from normal logic programs with constraints under the answer set semantics to propositional logic. Given a normal logic program, we show that by adding, for each loop in the program, a corresponding loop formula to the program's completion, we obtain a one-to-one correspondence between the answer sets of the program and the models of the resulting propositional theory. In the worst case, there may be an exponential number of loops in a logic program. To address this problem, we propose an approach that adds loop formulas a few at a time, selectively. Based on these results, we implement a system called ASSAT(X), depending on the SAT solver X used, for computing one answer set of a normal logic program with constraints. We test the system on a variety of benchmarks including the graph coloring, the blocks world planning, and Hamiltonian Circuit domains. Our experimental results show that in these domains, for the task of generating one answer set of a normal logic program, our system has a clear edge over the state-of-art answer set programming systems Smodels and DLV.

show abstract

Section: Introductionmentioning

confidence: 99%

ASSAT: computing answer sets of a logic program by SAT solvers

Lin

Zhao

2004

Artificial Intelligence

301

336

View full text Add to dashboard Cite

show abstract

“…there is a rule of the form (12) in P , such that u = hd(r), and either v or not v ∈ lit(W (A i )), for some i (1 ≤ i ≤ n). …”

Section: Loop Formulasmentioning

confidence: 99%

“…Only when a model of completion is generated which fails to be a stable model, the loop formula for a loop that caused the failure is constructed. In many cases, loop formulas need not be constructed at all [12]. In contrast, ranking constraints are introduced for rules in a given program, no matter whether there actually exist loops or not, or whether a loop contributes to the generation of a model of completion which is not a stable model.…”

Section: ⊓ ⊔mentioning

confidence: 99%

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

You

2010

Fundamenta Informaticae

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…(2) Many important NP-complete problems can be easily encoded as (negative) two-literal programs (Huang et al 2002). (3) Negative two-literal programs allow us to conduct large scale experiments with existing ASP solvers, such as smodels, dlv and clasp.…”

Section: Introductionmentioning

confidence: 99%

Random logic programs: Linear model

Wang

Wen

2014

Theory and Practice of Logic Programming

View full text Add to dashboard Cite

This paper proposes a model, the linear model, for randomly generating logic programs with low density of rules and investigates statistical properties of such random logic programs. It is mathematically shown that the average number of answer sets for a random program converges to a constant when the number of atoms approaches infinity. Several experimental results are also reported, which justify the suitability of the linear model. It is also experimentally shown that, under this model, the size distribution of answer sets for random programs tends to a normal distribution when the number of atoms is sufficiently large.

show abstract

Two-Literal Logic Programs and Satisfiability Representation of Stable Models: A Comparison

Cited by 5 publications

References 14 publications

ASSAT: computing answer sets of a logic program by SAT solvers

ASSAT: computing answer sets of a logic program by SAT solvers

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

Random logic programs: Linear model

Contact Info

Product

Resources

About