Fuzzy Answer Set Programming

Although Answer Set Programming (ASP) is a powerful framework for declarative problem solving, it cannot in an intuitive way handle situations in which some rules are uncertain, or in which it is more important to satisfy some constraints than others. Possibilistic ASP (PASP) is a natural extension of ASP in which certainty weights are associated with each rule. In this paper we contrast two different views on interpreting the weights attached to rules. Under the first view, weights reflect the certainty with which we can conclude the head of a rule when its body is satisfied. Under the second view, weights reflect the certainty that a given rule restricts the considered epistemic states of an agent in a valid way, i.e. it is the certainty that the rule itself is correct. The first view gives rise to a set of weighted answer sets, whereas the second view gives rise to a weighted set of classical answer sets.

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“…Fuzzy ASP (FASP) [47] is a generalization of ASP where the truth of literals is graded, i.e. literals are no longer strictly true or false.…”

Section: Related Workmentioning

confidence: 99%

“…In addition, extensions of FASP have been considered, e.g. aggregated FASP [47], that further extend the modeling power of FASP. Clearly, FASP is a powerful tool for the treatment of gradual information in the presence of complete information.…”

Section: Related Workmentioning

confidence: 99%

Semantics for possibilistic answer set programs: Uncertain rules versus rules with uncertain conclusions

Bauters

Schockaert

Cock

et al. 2014

International Journal of Approximate Reasoning

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“…ASP with choice rules, weighted sum, max, min etc, (see (Calimeri et al 2013) for a recent standardization of the ASP language) are easily expressible as BFASPs. Similar, Constraint Answer Set Programming (CASP) (Gebser et al 2009) and even Fuzzy ASP (FASP) (Nieuwenborgh et al 2006;Blondeel et al 2013) can all be expressed directly as BFASP instances. In CASP, all rules are of the form: a ← p 1 ∧ .…”

Section: Related Workmentioning

confidence: 99%

Stable model semantics for founded bounds

Aziz¹,

Chu²,

Stuckey³

2013

Theory and Practice of Logic Programming

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Answer Set Programming (ASP) is a powerful form of declarative programming used in areas such as planning or reasoning. ASP solvers enforce stable model semantics, which rule out solutions representing certain kinds of circular reasoning. Unfortunately, current ASP solvers are incapable of solving problems involving cyclic dependencies between multiple integer or continuous quantities effectively. In this paper, we generalize the notion of stable models to bound founded variables with arbitrary domains, where bounds on such variables need to be justified by some rule in the program in order for the model to be stable. We show how to handle significantly more general rule forms where bound founded variables can act as head or body variables, and where head and body variables can be related via complex constraints subject to certain monotonicity requirements. We describe a new unfounded set detection algorithm which allows us to enforce this generalization of the stable model semantics. We also show how these unfounded sets can be explained in order to allow effective conflict-directed clause learning. The new solver merges the best features of CP, SAT and ASP solvers and allows new types of problems to be solved very efficiently.

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“…In [18,17] both formalisms, i.e. ASP and fuzzy logic, have been combined into the single framework of fuzzy answer set programming (FASP) to increase the flexibility and hence the application potential of ASP.…”

Section: Introductionmentioning

confidence: 99%

“…Similarly, a more flexible interpretation of negation as failure is allowed and a rule can be satisfied to a certain degree. While [18] defines the semantics in a direct fashion, similar to the normal ASP semantics, [17] adapts the notion of an unfounded set to the setting of fuzzy interpretations.…”

Section: Introductionmentioning

confidence: 99%

Computing Fuzzy Answer Sets Using dlvhex

2007

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Abstract. Fuzzy answer set programming has been introduced as a framework that successfully combines the concepts of answer set programming and fuzzy logic. In this paper, we show how the fuzzy answer set semantics can be mapped onto the semantics for HEX-programs, which are nonmonotonic logic programs under the answer set semantics that support the use of external function calls. By using the DLVHEX reasoning engine, we so devise a vehicle for effectively computing fuzzy answer sets.

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Fuzzy Answer Set Programming

Cited by 10 publications

References 25 publications

Semantics for possibilistic answer set programs: Uncertain rules versus rules with uncertain conclusions

Semantics for possibilistic answer set programs: Uncertain rules versus rules with uncertain conclusions

Stable model semantics for founded bounds

Computing Fuzzy Answer Sets Using dlvhex

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