Stable Models for Temporal Theories

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.

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The interpretation of unsolvable λ-terms in models of untyped λ-calculus

Journal of Symbolic Logic ◽

10.2307/2586665 ◽

1998 ◽

Vol 63 (4) ◽

pp. 1529-1548 ◽

Cited By ~ 4

Author(s):

Rainer Kerth

Keyword(s):

Graph Model ◽

Stable Model ◽

Graph Models ◽

Stable Models

AbstractOur goal in this paper is to analyze the interpretation of arbitrary unsolvable λ-terms in a given model of λ-calculus. We focus on graph models and (a special type of) stable models. We introduce the syntactical notion of a decoration and the semantical notion of a critical sequence. We conjecture that any unsolvable term β-reduces to a term admitting a decoration. The main result of this paper concerns the interconnection between those two notions: given a graph model or stable model , we show that any unsolvable term admitting a decoration and having a non-empty interpretation in generates a critical sequence in the model.In the last section, we examine three classical graph models, namely the model of Plotkin and Scott, Engeler's model and Park's model . We show that and do not contain critical sequences whereas does.

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Stable models and non-determinism in logic programs with negation

Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '90 ◽

10.1145/298514.298572 ◽

1990 ◽

Cited By ~ 122

Author(s):

Domenico Sacca ◽

Carlo Zaniolo

Keyword(s):

Logic Programs ◽

Stable Models

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Stable Models in Testable Asset Pricing

Approximation, Probability, and Related Fields ◽

10.1007/978-1-4615-2494-6_17 ◽

1994 ◽

pp. 223-235 ◽

Cited By ~ 2

Author(s):

Bertrand Gamrowski ◽

Svetlozar T. Rachev

Keyword(s):

Asset Pricing ◽

Stable Models

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Discrete multivariable systems approximation by minimal pade type stable models

10.1109/cdc.1982.268321 ◽

1982 ◽

Cited By ~ 1

Author(s):

Y. Bistritz ◽

U. Shaked

Keyword(s):

Multivariable Systems ◽

Stable Models

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Greedy algorithms in Datalog

Theory and Practice of Logic Programming ◽

10.1017/s1471068401001090 ◽

2001 ◽

Vol 1 (4) ◽

pp. 381-407 ◽

Cited By ~ 11

Author(s):

SERGIO GRECO ◽

CARLO ZANIOLO

Keyword(s):

Optimization Problems ◽

Greedy Algorithms ◽

Design Of Algorithms ◽

Effective Implementation ◽

Implementation Techniques ◽

Research Challenge ◽

Storage Structures ◽

Selection Of ◽

Stable Models

In the design of algorithms, the greedy paradigm provides a powerful tool for solving efficiently classical computational problems, within the framework of procedural languages. However, expressing these algorithms within the declarative framework of logic-based languages has proven a difficult research challenge. In this paper, we extend the framework of Datalog-like languages to obtain simple declarative formulations for such problems, and propose effective implementation techniques to ensure computational complexities comparable to those of procedural formulations. These advances are achieved through the use of the choice construct, extended with preference annotations to effect the selection of alternative stable-models and nondeterministic fixpoints. We show that, with suitable storage structures, the differential fixpoint computation of our programs matches the complexity of procedural algorithms in classical search and optimization problems.

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