Extending Disjunctive Logic Programming by T-norms

Mateis, Cristinel

doi:10.1007/3-540-46767-x_21

Cited by 12 publications

(7 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The implication based approach in [17] adheres closer to ours. A rule of the form α z ← β is said to be satisfied by the interpretation iff (in our notation) I |= (α) ≥ L T (I |= (β), z).…”

Section: Related Worksupporting

confidence: 52%

“…A rule of the form α z ← β is said to be satisfied by the interpretation iff (in our notation) I |= (α) ≥ L T (I |= (β), z). The residuation principle reveals a clear connection with our approach when committing to an R-implicator I T : namely that I satisfies the rule α z ← β according to [17] iff I satisfies this rule at least to degree z in our approach. This is also in accordance with [9] where the use of adjoint pairs (T , I T ) is strongly advocated to preserve important theoretical results.…”

Section: Related Workmentioning

confidence: 91%

See 1 more Smart Citation

An introduction to fuzzy answer set programming

Nieuwenborgh

Cock

Vermeir

2007

Ann Math Artif Intell

View full text Add to dashboard Cite

In this paper we show how the concepts of answer set programming and fuzzy logic can be successfully combined into the single framework of fuzzy answer set programming (FASP). The framework offers the best of both worlds: from the answer set semantics, it inherits the truly declarative non-monotonic reasoning capabilities while, on the other hand, the notions from fuzzy logic in the framework allow it to step away from the sharp principles used in classical logic, e.g., that something is either completely true or completely false. As fuzzy logic gives the user great flexibility regarding the choice for the interpretation of the notions of negation, conjunction, disjunction and implication, the FASP framework is highly configurable and can, e.g., be tailored to any specific area of application. Finally, the presented framework turns out to be a proper extension of classical answer set programming, as we show, in contrast to other proposals in the literature, that there are only minor restrictions one has to demand on the fuzzy operations used, in order to be able to retrieve the classical semantics using FASP.

show abstract

Section: Related Worksupporting

confidence: 52%

Section: Related Workmentioning

confidence: 91%

An introduction to fuzzy answer set programming

Nieuwenborgh

Cock

Vermeir

2007

Ann Math Artif Intell

View full text Add to dashboard Cite

show abstract

“…So, we think that this approach is far from the spirit of possibilistic logic. In the same way, [34] proposes a general framework extending disjunctive programs and stable models semantics by introducing a reliability interval for each rule. From a syntactic point of view, our approach can be considered as a particular case of this one.…”

Section: Dealing With Default Reasoning and Uncertaintymentioning

confidence: 99%

Possibilistic uncertainty handling for answer set programming

Pichon

Garcia

Stéphan

et al. 2006

Ann Math Artif Intell

164

View full text Add to dashboard Cite

In this work, we introduce a new framework able to deal with a reasoning that is at the same time non monotonic and uncertain. In order to take into account a certainty level associated to each piece of knowledge, we use possibility theory to extend the non monotonic semantics of stable models for logic programs with default negation. By means of a possibility distribution we define a clear semantics of such programs by introducing what is a possibilistic stable model. We also propose a syntactic process based on a fix-point operator to compute these particular models representing the deductions of the program and their certainty. Then, we show how this introduction of a certainty level on each rule of a program can be used in order to restore its consistency in case of the program has no model at all. Furthermore, we explain how we can compute possibilistic stable models by using available softwares for Answer Set Programming and we describe the main lines of the system that we have developed to achieve this goal.

show abstract

“…[174] provides an even more general setting as the function f may also depend on the variables occurring in the rule body. On the other hand there are also some extensions to many-valued disjunctive logic programs [186,187,253]. In some cases, e.g.…”

Section: If a Nodementioning

confidence: 99%

“…[35,122,130,252,276]. On the other hand, there are very few works dealing with normal logic programs [38,78,80,142,143,144,145,146,147,148,173,186,250,253,258,263], and little is know about top-down query answering procedures. The only exceptions are [250,258,263].…”

Section: If a Nodementioning

confidence: 99%