scholarly journals Extending Well-Founded Semantics with Clark’s Completion for Disjunctive Logic Programs

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Juan Carlos Nieves ◽  
Mauricio Osorio
Keyword(s):  
Aggregation Operator ◽  
Stable Model ◽  
Logic Programs ◽  
Complete Lattices ◽  
Transformation Rules ◽  
Disjunctive Program ◽  
Stable Semantics ◽  
Disjunctive Logic Programs ◽  
Disjunctive Programs ◽  
Explicit Negation

In this paper, we introduce new semantics (that we call D3-WFS-DCOMP) and compare it with the stable semantics (STABLE). For normal programs, this semantics is based onsuitableintegration of the well-founded semantics (WFS) and the Clark’s completion. D3-WFS-DCOM has the following appealing properties: First, it agrees with STABLE in the sense that it never defines a nonminimal model or a nonminimal supported model. Second, for normal programs it extends WFS. Third, every stable model of a disjunctive programPis a D3-WFS-DCOM model ofP. Fourth, it is constructed using transformation rules accepted by STABLE. We also introduce second semantics that we call D2-WFS-DCOMP. We show that D2-WFS-DCOMP is equivalent to D3-WFS-DCOMP for normal programs but this is not the case for disjunctive programs. We also introduce third new semantics that supports the use of implicit disjunctions. We illustrate how these semantics can be extended to programs including explicit negation, default negation in the head of a clause, and aluboperator, which is a generalization of the aggregation operatorsetofover arbitrary complete lattices.

scholarly journals Justifications for programs with disjunctive and causal-choice rules

2016 ◽  
Vol 16 (5-6) ◽  
pp. 587-603 ◽  
Author(s):  
PEDRO CABALAR ◽  
JORGE FANDINNO
Keyword(s):  
Choice Rule ◽  
Algebraic Expression ◽  
Stable Model ◽  
Logic Programs ◽  
Causal Information ◽  
Disjunctive Logic Programs ◽  
New Type ◽  
Algebraic Operations ◽  
Disjunctive Programs ◽  
Stable Models

AbstractIn this paper, we study an extension of the stable model semantics for disjunctive logic programs where each true atom in a model is associated with an algebraic expression (in terms of rule labels) that represents its justifications. As in our previous work for non-disjunctive programs, these justifications are obtained in a purely semantic way, by algebraic operations (product, addition and application) on a lattice of causal values. Our new definition extends the concept ofcausal stable modelto disjunctive logic programs and satisfies that each (standard) stable model corresponds to a disjoint class of causal stable models sharing the same truth assignments, but possibly varying the obtained explanations. We provide a pair of illustrative examples showing the behaviour of the new semantics and discuss the need of introducing a new type of rule, which we callcausal-choice. This type of rule intuitively captures the idea of “Amay causeB” and, when causal information is disregarded, amounts to a usual choice rule under the standard stable model semantics.

Disjunctive logic programs with existential quantification in rule heads

2013 ◽  
Vol 13 (4-5) ◽  
pp. 563-578 ◽  
Author(s):  
JIA-HUAI YOU ◽  
HENG ZHANG ◽  
YAN ZHANG
Keyword(s):  
Stable Model ◽  
Logic Programs ◽  
Disjunctive Logic Programs ◽  
Decidable Fragment ◽  
Definition Of ◽  
Existential Quantification ◽  
Disjunctive Programs ◽  
Second Order Logic ◽  
Stable Models

AbstractWe consider disjunctive logic programs without function symbols but with existential quantification in rule heads, under the semantics of general stable models. There are at least two interesting prospects in these programs. The first is that a program can be made more succinct by using existential variables, and the second is on the potential in representing defeasible ontological knowledge by these logic programs. This paper studies some of the properties of these programs. First, we show a simple yet intuitive definition of stable models for these programs that does not resort to second-order logic. Second, the stable models of these programs can be characterized by an extension of progression for disjunctive programs, which provides a native characterization of justification for stable models. We then study the decidability issue. While the stable model existence problem for safe disjunctive programs is decidable, with existential quantification allowed in rule heads the problem becomes undecidable. We identify an interesting decidable fragment by exploring a new notion of stratification over existential quantification.

Well-Founded Semantics Coincides with Three-Valued Stable Semantics1

1990 ◽  
Vol 13 (4) ◽  
pp. 445-463
Author(s):  
Teodor Przymusinski
Keyword(s):  
Logic Program ◽  
Natural Extension ◽  
Natural Generalization ◽  
Stable Model ◽  
Logic Programs ◽  
Default Theory ◽  
Recent Approach ◽  
Stable Semantics ◽  
Disjunctive Logic Programs ◽  
Stable Models

We introduce 3-valued stable models which are a natural generalization of standard (2-valued) stable models. We show that every logic program P has at least one 3-valued stable model and that the well-founded model of any program P [Van Gelder et al., 1990] coincides with the smallest 3-valued stable model of P. We conclude that the well-founded semantics of an arbitrary logic program coincides with the 3-valued stable model semantics. The 3-valued stable semantics is closely related to non-monotonic formalisms in AI. Namely, every program P can be translated into a suitable autoepistemic (resp. default) theory P ˆ so that the 3-valued stable semantics of P coincides with the (3-valued) autoepistemic (resp. default) semantics of P ˆ. Similar results hold for circumscription and CWA. Moreover, it can be shown that the 3-valued stable semantics has a natural extension to the class of all disjunctive logic programs and deductive databases. Finally, following upon the recent approach developed by Gelfond and Lifschitz, we extend all of our results to more general logic programs which, in addition to the use of negation as failure, permit the use of classical negation.

scholarly journals Trichotomy and dichotomy results on the complexity of reasoning with disjunctive logic programs

2010 ◽  
Vol 11 (6) ◽  
pp. 881-904 ◽  
Author(s):  
MIROSŁAW TRUSZCZYŃSKI
Keyword(s):  
The Other ◽  
Logic Programs ◽  
Finite Representation ◽  
Potential Interest ◽  
Disjunctive Logic Programs ◽  
Problem Instances ◽  
The One ◽  
Answer Sets ◽  
Disjunctive Programs ◽  
Credulous Reasoning

AbstractWe present trichotomy results characterizing the complexity of reasoning with disjunctive logic programs. To this end, we introduce a certain definition schema for classes of programs based on a set of allowed arities of rules. We show that each such class of programs has a finite representation, and for each of the classes definable in the schema, we characterize the complexity of the existence of an answer set problem. Next, we derive similar characterizations of the complexity of skeptical and credulous reasoning with disjunctive logic programs. Such results are of potential interest. On the one hand, they reveal some reasons responsible for the hardness of computing answer sets. On the other hand, they identify classes of problem instances, for which the problem is “easy” (in P) or “easier than in general” (in NP). We obtain similar results for the complexity of reasoning with disjunctive programs under the supported-model semantics.

scholarly journals Modularity Aspects of Disjunctive Stable Models

2009 ◽  
Vol 35 ◽  
pp. 813-857 ◽  
Author(s):  
T. Janhunen ◽  
E. Oikarinen ◽  
H. Tompits ◽  
S. Woltran
Keyword(s):  
Programming Languages ◽  
Connected Components ◽  
Stable Model ◽  
Logic Programs ◽  
Strongly Connected Components ◽  
Verification Method ◽  
Strongly Connected ◽  
Disjunctive Logic Programs ◽  
Mutual Comparison ◽  
Output Interface

Practically all programming languages allow the programmer to split a program into several modules which brings along several advantages in software development. In this paper, we are interested in the area of answer-set programming where fully declarative and nonmonotonic languages are applied. In this context, obtaining a modular structure for programs is by no means straightforward since the output of an entire program cannot in general be composed from the output of its components. To better understand the effects of disjunctive information on modularity we restrict the scope of analysis to the case of disjunctive logic programs (DLPs) subject to stable-model semantics. We define the notion of a DLP-function, where a well-defined input/output interface is provided, and establish a novel module theorem which indicates the compositionality of stable-model semantics for DLP-functions. The module theorem extends the well-known splitting-set theorem and enables the decomposition of DLP-functions given their strongly connected components based on positive dependencies induced by rules. In this setting, it is also possible to split shared disjunctive rules among components using a generalized shifting technique. The concept of modular equivalence is introduced for the mutual comparison of DLP-functions using a generalization of a translation-based verification method.

scholarly journals Semantics for Possibilistic Disjunctive Programs

2011 ◽  
Vol 13 (1) ◽  
pp. 33-70 ◽  
Author(s):  
JUAN CARLOS NIEVES ◽  
MAURICIO OSORIO ◽  
ULISES CORTÉS
Keyword(s):  
Logic Programming ◽  
Knowledge Base ◽  
Logic Program ◽  
Programming Approach ◽  
Logic Programs ◽  
Possibilistic Logic ◽  
Point Operator ◽  
Disjunctive Logic Programs ◽  
Answer Sets ◽  
Disjunctive Programs

AbstractIn this paper, a possibilistic disjunctive logic programming approach for modeling uncertain, incomplete, and inconsistent information is defined. This approach introduces the use of possibilistic disjunctive clauses, which are able to capture incomplete information and states of a knowledge base at the same time. By considering a possibilistic logic program as a possibilistic logic theory, a construction of a possibilistic logic programming semantic based on answer sets and the proof theory of possibilistic logic is defined. It shows that this possibilistic semantics for disjunctive logic programs can be characterized by a fixed-point operator. It is also shown that the suggested possibilistic semantics can be computed by a resolution algorithm and the consideration of optimal refutations from a possibilistic logic theory. In order to manage inconsistent possibilistic logic programs, a preference criterion between inconsistent possibilistic models is defined. In addition, the approach of cuts for restoring consistency of an inconsistent possibilistic knowledge base is adopted. The approach is illustrated in a medical scenario.

scholarly journals Thirty years of Epistemic Specifications

2021 ◽  
pp. 1-41
Author(s):  
JORGE FANDINNO ◽  
WOLFGANG FABER ◽  
MICHAEL GELFOND
Keyword(s):  
State Of The Art ◽  
World View ◽  
Formal Semantics ◽  
Future Research ◽  
Knowledge Representation And Reasoning ◽  
Stable Model ◽  
Logic Programs ◽  
Current State ◽  
Closed World ◽  
Disjunctive Logic Programs

Abstract The language of epistemic specifications and epistemic logic programs extends disjunctive logic programs under the stable model semantics with modal constructs called subjective literals. Using subjective literals, it is possible to check whether a regular literal is true in every or some stable models of the program, those models, in this context also called belief sets, being collected in a set called world view. This allows for representing, within the language, whether some proposition should be understood accordingly to the open or the closed world assumption. Several attempts for capturing the intuitions underlying the language by means of a formal semantics were given, resulting in a multitude of proposals that makes it difficult to understand the current state of the art. In this article, we provide an overview of the inception of the field and the knowledge representation and reasoning tasks it is suitable for. We also provide a detailed analysis of properties of proposed semantics, and an outlook of challenges to be tackled by future research in the area.

scholarly journals On elementary loops of logic programs

2011 ◽  
Vol 11 (6) ◽  
pp. 953-988 ◽  
Author(s):  
MARTIN GEBSER ◽  
JOOHYUNG LEE ◽  
YULIYA LIERLER
Keyword(s):  
Nonmonotonic Reasoning ◽  
The Body ◽  
The Other ◽  
Stable Model ◽  
Logic Programs ◽  
Graph Theoretic ◽  
Theoretic Characterization ◽  
Definition Of ◽  
Disjunctive Programs

AbstractUsing the notion of an elementary loop, Gebser and Schaub (2005. Proceedings of the Eighth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'05), 53–65) refined the theorem on loop formulas attributable to Lin and Zhao (2004) by considering loop formulas of elementary loops only. In this paper, we reformulate the definition of an elementary loop, extend it to disjunctive programs, and study several properties of elementary loops, including how maximal elementary loops are related to minimal unfounded sets. The results provide useful insights into the stable model semantics in terms of elementary loops. For a nondisjunctive program, using a graph-theoretic characterization of an elementary loop, we show that the problem of recognizing an elementary loop is tractable. On the other hand, we also show that the corresponding problem is coNP-complete for a disjunctive program. Based on the notion of an elementary loop, we present the class of Head-Elementary-loop-Free (HEF) programs, which strictly generalizes the class of Head-Cycle-Free (HCF) programs attributable to Ben-Eliyahu and Dechter (1994. Annals of Mathematics and Artificial Intelligence 12, 53–87). Like an HCF program, an HEF program can be turned into an equivalent nondisjunctive program in polynomial time by shifting head atoms into the body.

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