scholarly journals Anytime answer set optimization via unsatisfiable core shrinking

2016 ◽  
Vol 16 (5-6) ◽  
pp. 533-551 ◽  
Author(s):  
MARIO ALVIANO ◽  
CARMINE DODARO
Keyword(s):  
Set Optimization ◽  
Core Analysis ◽  
Logic Programs ◽  
Anytime Algorithm ◽  
Shrinking Process ◽  
The One ◽  
Weak Constraints ◽  
Unsatisfiable Core ◽  
Stable Models ◽  
Answer Set

AbstractUnsatisfiable core analysis can boost the computation of optimum stable models for logic programs with weak constraints. However, current solvers employing unsatisfiable core analysis either run to completion, or provide no suboptimal stable models but the one resulting from the preliminary disjoint cores analysis. This drawback is circumvented here by introducing a progression based shrinking of the analyzed unsatisfiable cores. In fact, suboptimal stable models are possibly found while shrinking unsatisfiable cores, hence resulting into an anytime algorithm. Moreover, as confirmed empirically, unsatisfiable core analysis also benefits from the shrinking process in terms of solved instances.

scholarly journals Unsatisfiable Core Shrinking for Anytime Answer Set Optimization

2017 ◽  
Author(s):  
Mario Alviano ◽  
Carmine Dodaro
Keyword(s):  
Efficient Algorithms ◽  
Set Optimization ◽  
Core Analysis ◽  
Anytime Algorithm ◽  
Original Algorithm ◽  
Unsatisfiable Core ◽  
Stable Models ◽  
Answer Set

Efficient algorithms for the computation of optimum stable models are based on unsatisfiable core analysis. However, these algorithms essentially run to completion, providing few or even no suboptimal stable models. This drawback can be circumvented by shrinking unsatisfiable cores. Interestingly, the resulting anytime algorithm can solve more instances than the original algorithm.

Unsatisfiable Core Analysis and Aggregates for Optimum Stable Model Search

2020 ◽  
Vol 176 (3-4) ◽  
pp. 271-297
Author(s):  
Mario Alviano ◽  
Carmine Dodaro
Keyword(s):  
State Of The Art ◽  
Answer Set Programming ◽  
Efficient Algorithms ◽  
Satisfiability Problem ◽  
Core Analysis ◽  
Stable Model ◽  
Maximum Satisfiability ◽  
Model Search ◽  
Unsatisfiable Core ◽  
Stable Models

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.

scholarly journals A program-level approach to revising logic programs under the answer set semantics

2010 ◽  
Vol 10 (4-6) ◽  
pp. 565-580 ◽  
Author(s):  
JAMES P. DELGRANDE
Keyword(s):  
Logic Program ◽  
Fundamental Principle ◽  
Logic Programs ◽  
Minimal Set ◽  
Essential Idea ◽  
The One ◽  
Answer Set Semantics ◽  
Answer Sets ◽  
Update Logic ◽  
Answer Set

AbstractAn approach to the revision of logic programs under the answer set semantics is presented. For programs P and Q, the goal is to determine the answer sets that correspond to the revision of P by Q, denoted P * Q. A fundamental principle of classical (AGM) revision, and the one that guides the approach here, is the success postulate. In AGM revision, this stipulates that α ∈ K * α. By analogy with the success postulate, for programs P and Q, this means that the answer sets of Q will in some sense be contained in those of P * Q. The essential idea is that for P * Q, a three-valued answer set for Q, consisting of positive and negative literals, is first determined. The positive literals constitute a regular answer set, while the negated literals make up a minimal set of naf literals required to produce the answer set from Q. These literals are propagated to the program P, along with those rules of Q that are not decided by these literals. The approach differs from work in update logic programs in two main respects. First, we ensure that the revising logic program has higher priority, and so we satisfy the success postulate; second, for the preference implicit in a revision P * Q, the program Q as a whole takes precedence over P, unlike update logic programs, since answer sets of Q are propagated to P. We show that a core group of the AGM postulates are satisfied, as are the postulates that have been proposed for update logic programs.

scholarly journals On the Semantics of Logic Programs with Preferences

2007 ◽  
Vol 30 ◽  
pp. 501-523 ◽  
Author(s):  
S. Greco ◽  
I. Trubitsyna ◽  
E. Zumpano
Keyword(s):  
Logic Programming ◽  
Complexity Analysis ◽  
Structural Information ◽  
Logic Program ◽  
Set Optimization ◽  
Logic Programs ◽  
Preference Relations ◽  
New Interpretation ◽  
Semantics Of Logic Programs ◽  
Stable Models

This work is a contribution to prioritized reasoning in logic programming in the presence of preference relations involving atoms. The technique, providing a new interpretation for prioritized logic programs, is inspired by the semantics of Prioritized Logic Programming and enriched with the use of structural information of preference of Answer Set Optimization Programming. Specifically, the analysis of the logic program is carried out together with the analysis of preferences in order to determine the choice order and the sets of comparable models. The new semantics is compared with other approaches known in the literature and complexity analysis is also performed, showing that, with respect to other similar approaches previously proposed, the complexity of computing preferred stable models does not increase.

scholarly journals Temporal logic programs with variables

2016 ◽  
Vol 17 (2) ◽  
pp. 226-243 ◽  
Author(s):  
FELICIDAD AGUADO ◽  
PEDRO CABALAR ◽  
GILBERTO PÉREZ ◽  
CONCEPCIÓN VIDAL ◽  
MARTÍN DIÉGUEZ
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Logic Program ◽  
Answer Set Programming ◽  
Logic Programs ◽  
First Order ◽  
Linear Time Temporal Logic ◽  
Definition Of ◽  
Stable Models ◽  
Answer Set

AbstractIn this note, we consider the problem of introducing variables in temporal logic programs under the formalism of Temporal Equilibrium Logic, an extension of Answer Set Programming for dealing with linear-time modal operators. To this aim, we provide a definition of a first-order version of Temporal Equilibrium Logic that shares the syntax of first-order Linear-time Temporal Logic but has different semantics, selecting some Linear-time Temporal Logic models we call temporal stable models. Then, we consider a subclass of theories (called splittable temporal logic programs) that are close to usual logic programs but allowing a restricted use of temporal operators. In this setting, we provide a syntactic definition of safe variables that suffices to show the property of domain independence – that is, addition of arbitrary elements in the universe does not vary the set of temporal stable models. Finally, we present a method for computing the derivable facts by constructing a non-temporal logic program with variables that is fed to a standard Answer Set Programming grounder. The information provided by the grounder is then used to generate a subset of ground temporal rules which is equivalent to (and generally smaller than) the full program instantiation.

scholarly journals Module theorem for the general theory of stable models

2012 ◽  
Vol 12 (4-5) ◽  
pp. 719-735 ◽  
Author(s):  
JOSEPH BABB ◽  
JOOHYUNG LEE
Keyword(s):  
General Theory ◽  
General Class ◽  
Answer Set Programming ◽  
Splitting Theorem ◽  
Logic Programs ◽  
Input Output ◽  
Answer Sets ◽  
Output Interface ◽  
Stable Models ◽  
Answer Set

AbstractThe module theorem by Janhunen et al. demonstrates how to provide a modular structure in answer set programming, where each module has a well-defined input/output interface which can be used to establish the compositionality of answer sets. The theorem is useful in the analysis of answer set programs, and is a basis of incremental grounding and reactive answer set programming. We extend the module theorem to the general theory of stable models by Ferraris et al. The generalization applies to non-ground logic programs allowing useful constructs in answer set programming, such as choice rules, the count aggregate, and nested expressions. Our extension is based on relating the module theorem to the symmetric splitting theorem by Ferraris et al. Based on this result, we reformulate and extend the theory of incremental answer set computation to a more general class of programs.

scholarly journals Linear-Time Temporal Answer Set Programming

2021 ◽  
pp. 1-55
Author(s):  
FELICIDAD AGUADO ◽  
PEDRO CABALAR ◽  
MARTÍN DIÉGUEZ ◽  
GILBERTO PÉREZ ◽  
TORSTEN SCHAUB ◽  
...  
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Selection Criterion ◽  
Answer Set Programming ◽  
Logic Programs ◽  
Modal Operators ◽  
Linear Time Temporal Logic ◽  
Stable Models ◽  
Answer Set

Abstract In this survey, we present an overview on (Modal) Temporal Logic Programming in view of its application to Knowledge Representation and Declarative Problem Solving. The syntax of this extension of logic programs is the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). In the paper, we focus on the main recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL but involves a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). As a result, we obtain a proper extension of the stable models semantics for the general case of temporal formulas in the syntax of LTL. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between finite and infinite trace length. We also provide further useful results, such as the translation into other formalisms like Quantified Equilibrium Logic and Second-order LTL, and some techniques for computing temporal stable models based on automata constructions. In the remainder of the paper, we focus on practical aspects, defining a syntactic fragment called (modal) temporal logic programs closer to ASP, and explaining how this has been exploited in the construction of the solver telingo, a temporal extension of the well-known ASP solver clingo that uses its incremental solving capabilities.

scholarly journals Logic programs with monotone abstract constraint atoms

2008 ◽  
Vol 8 (2) ◽  
pp. 167-199 ◽  
Author(s):  
VICTOR W. MAREK ◽  
ILKKA NIEMELÄ ◽  
MIROSŁAW TRUSZCZYŃSKI
Keyword(s):  
Logic Programming ◽  
Logic Programs ◽  
Common Generalization ◽  
One Step ◽  
Normal Logic ◽  
The One ◽  
Operational Concept ◽  
Stable Models

AbstractWe introduce and study logic programs whose clauses are built out of monotone constraint atoms. We show that the operational concept of the one-step provability operator generalizes to programs with monotone constraint atoms, but the generalization involves nondeterminism. Our main results demonstrate that our formalism is a common generalization of (1) normal logic programming with its semantics of models, supported models and stable models, (2) logic programming with weight atoms lparse programs) with the semantics of stable models, as defined by Niemelä, Simons and Soininen, and (3) of disjunctive logic programming with the possible-model semantics of Sakama and Inoue.

scholarly journals Relating Multi-Adjoint Normal Logic Programs to Core Fuzzy Answer Set Programs from a Semantical Approach

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 881
Author(s):  
M. Eugenia Cornejo ◽  
David Lobo ◽  
Jesús Medina
Keyword(s):  
Fuzzy Logic ◽  
Logic Programming ◽  
Programming Language ◽  
Answer Set Programming ◽  
Logic Programs ◽  
The Core ◽  
Normal Logic ◽  
Answer Sets ◽  
Stable Models ◽  
Answer Set

This paper relates two interesting paradigms in fuzzy logic programming from a semantical approach: core fuzzy answer set programming and multi-adjoint normal logic programming. Specifically, it is shown how core fuzzy answer set programs can be translated into multi-adjoint normal logic programs and vice versa, preserving the semantics of the starting program. This translation allows us to combine the expressiveness of multi-adjoint normal logic programming with the compactness and simplicity of the core fuzzy answer set programming language. As a consequence, theoretical properties and results which relate the answer sets to the stable models of the respective logic programming frameworks are obtained. Among others, this study enables the application of the existence theorem of stable models developed for multi-adjoint normal logic programs to ensure the existence of answer sets in core fuzzy answer set programs.

scholarly journals Reformulating the Situation Calculus and the Event Calculus in the General Theory of Stable Models and in Answer Set Programming

2012 ◽  
Vol 43 ◽  
pp. 571-620 ◽  
Author(s):  
J. Lee ◽  
R. Palla
Keyword(s):  
General Theory ◽  
Situation Calculus ◽  
Stable Model ◽  
Logic Programs ◽  
Event Calculus ◽  
Action Languages ◽  
Canonical Formulas ◽  
Action Logics ◽  
Stable Models ◽  
Answer Set

Circumscription and logic programs under the stable model semantics are two well-known nonmonotonic formalisms. The former has served as a basis of classical logic based action formalisms, such as the situation calculus, the event calculus and temporal action logics; the latter has served as a basis of a family of action languages, such as language A and several of its descendants. Based on the discovery that circumscription and the stable model semantics coincide on a class of canonical formulas, we reformulate the situation calculus and the event calculus in the general theory of stable models. We also present a translation that turns the reformulations further into answer set programs, so that efficient answer set solvers can be applied to compute the situation calculus and the event calculus.

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