scholarly journals Properties and Applications of Programs with Monotone and Convex Constraints

2006 ◽  
Vol 27 ◽  
pp. 299-334 ◽  
Author(s):  
L. Liu ◽  
M. Truszczynski
Keyword(s):  
Logic Programming ◽  
Program Completion ◽  
Convex Constraints ◽  
Normal Logic ◽  
Stable Models

We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include the notions of strong and uniform equivalence with their characterizations, tight programs and Fages Lemma, program completion and loop formulas. Our results provide an abstract account of properties of some recent extensions of logic programming with aggregates, especially the formalism of lparse programs. They imply a method to compute stable models of lparse programs by means of off-the-shelf solvers of pseudo-boolean constraints, which is often much faster than the smodels system.

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 Interdefinability of defeasible logic and logic programming under the well-founded semantics

2011 ◽  
Vol 13 (1) ◽  
pp. 107-142 ◽  
Author(s):  
FREDERICK MAIER
Keyword(s):  
Logic Programming ◽  
Opposite Direction ◽  
Stable Model ◽  
Logic Programs ◽  
Defeasible Logic ◽  
Normal Logic

AbstractWe provide a method of translating theories of Nute's defeasible logic into logic programs, and a corresponding translation in the opposite direction. Under certain natural restrictions, the conclusions of defeasible theories under the ambiguity propagating defeasible logic ADL correspond to those of the well-founded semantics for normal logic programs, and so it turns out that the two formalisms are closely related. Using the same translation of logic programs into defeasible theories, the semantics for the ambiguity blocking defeasible logic NDL can be seen as indirectly providing an ambiguity blocking semantics for logic programs. We also provide antimonotone operators for both ADL and NDL, each based on the Gelfond–Lifschitz (GL) operator for logic programs. For defeasible theories without defeaters or priorities on rules, the operator for ADL corresponds to the GL operator and so can be seen as partially capturing the consequences according to ADL. Similarly, the operator for NDL captures the consequences according to NDL, though in this case no restrictions on theories apply. Both operators can be used to define stable model semantics for defeasible theories.

scholarly journals Well-founded and stable semantics of logic programs with aggregates

2007 ◽  
Vol 7 (3) ◽  
pp. 301-353 ◽  
Author(s):  
NIKOLAY PELOV ◽  
MARC DENECKER ◽  
MAURICE BRUYNOOGHE
Keyword(s):  
Logic Programming ◽  
Second Order ◽  
Logic Programs ◽  
Consequence Operator ◽  
Trade Offs ◽  
Stable Semantics ◽  
Consequence Operators ◽  
Semantics Of Logic Programs ◽  
Stable Models

AbstractIn this paper, we present a framework for the semantics and the computation of aggregates in the context of logic programming. In our study, an aggregate can be an arbitrary interpreted second order predicate or function. We define extensions of the Kripke-Kleene, the well-founded and the stable semantics for aggregate programs. The semantics is based on the concept of a three-valuedimmediate consequence operatorof an aggregate program. Such an operatorapproximatesthe standard two-valued immediate consequence operator of the program, and induces a unique Kripke-Kleene model, a unique well-founded model and a collection of stable models. We study different ways of defining such operators and thus obtain a framework of semantics, offering different trade-offs betweenprecisionandtractability. In particular, we investigate conditions on the operator that guarantee that the computation of the three types of semantics remains on the same level as for logic programs without aggregates. Other results show that, in practice, even efficient three-valued immediate consequence operators which are very low in the precision hierarchy, still provide optimal precision.

scholarly journals A Functorial Framework for Constraint Normal Logic Programming

2006 ◽  
pp. 555-577 ◽  
Author(s):  
Paqui Lucio ◽  
Fernando Orejas ◽  
Edelmira Pasarella ◽  
Elvira Pino
Keyword(s):  
Logic Programming ◽  
Normal Logic

scholarly journals Relating defeasible and normal logic programming through transformation properties

2003 ◽  
Vol 290 (1) ◽  
pp. 499-529 ◽  
Author(s):  
Carlos Iván Chesñevar ◽  
Jürgen Dix ◽  
Frieder Stolzenburg ◽  
G.R.Guillermo Ricardo Simari
Keyword(s):  
Logic Programming ◽  
Normal Logic

scholarly journals Lloyd-Topor completion and general stable models

2013 ◽  
Vol 13 (4-5) ◽  
pp. 503-515 ◽  
Author(s):  
VLADIMIR LIFSCHITZ ◽  
FANGKAI YANG
Keyword(s):  
Logic Program ◽  
Program Completion ◽  
Stable Model ◽  
First Order ◽  
The Relationship ◽  
Stable Models

AbstractWe investigate the relationship between the generalization of program completion defined in 1984 by Lloyd and Topor and the generalization of the stable model semantics introduced recently by Ferraris et al. The main theorem can be used to characterize, in some cases, the general stable models of a logic program by a first-order formula. The proof uses Truszczynski's stable model semantics of infinitary propositional formulas.

scholarly journals Complete Extensions in Argumentation Coincide with 3-Valued Stable Models in Logic Programming

Studia Logica ◽  
2009 ◽  
Vol 93 (2-3) ◽  
pp. 383-403 ◽  
Author(s):  
Yining Wu ◽  
Martin Caminada ◽  
Dov M. Gabbay
Keyword(s):  
Logic Programming ◽  
Stable Models

scholarly journals A Functorial Framework for Constraint Normal Logic Programming

2008 ◽  
Vol 16 (3) ◽  
pp. 421-450 ◽  
Author(s):  
P. Lucio ◽  
F. Orejas ◽  
E. Pasarella ◽  
E. Pino
Keyword(s):  
Logic Programming ◽  
Normal Logic

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.

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