Measuring Inconsistency in Fuzzy Answer Set Semantics

Madrid, Nicolás; Ojeda‐Aciego, Manuel

doi:10.1109/tfuzz.2011.2114669

Cited by 36 publications

(17 citation statements)

References 30 publications

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“…Hence we want to have I(l) ⊗ I(¬l) = 0 for each answer set I and each literal l. This is equivalent to I(l) + I(¬l) ≤ 1. Note that this definition of consistency coincides with the approach in [11]. The set of all atoms in P is denoted by B P .…”

Section: Fuzzy Answer Set Programming (Fasp)mentioning

confidence: 91%

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Complexity of fuzzy answer set programming under Łukasiewicz semantics

Blondeel

Schockaert

Vermeir

et al. 2014

International Journal of Approximate Reasoning

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Fuzzy answer set programming (FASP) is a generalization of answer set programming (ASP) in which propositions are allowed to be graded. Little is known about the computational complexity of FASP and almost no techniques are available to compute the answer sets of a FASP program. In this paper, we analyze the computational complexity of FASP under Lukasiewicz semantics. In particular we show that the complexity of the main reasoning tasks is located at the first level of the polynomial hierarchy, even for disjunctive FASP programs for which reasoning is classically located at the second level. Moreover, we show a reduction from reasoning with such FASP programs to bilevel linear programming, thus opening the door to practical applications. For definite FASP programs we can show P-membership. Surprisingly, when allowing disjunctions to occur in the body of rules -a syntactic generalization which does not affect the expressivity of ASP in the classical case -the picture changes drastically. In particular, reasoning tasks are then located at the second level of the polynomial hierarchy, while for simple FASP programs, we can only show that the unique answer set can be found in pseudo-polynomial time. Moreover, the connection to an existing open problem about integer equations suggests that the problem of fully

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Section: Fuzzy Answer Set Programming (Fasp)mentioning

confidence: 91%

“…[8,9,10,11,12,13,14]). The main differences are the type of connectives that are allowed, the truth lattices that are used, the definition of a model of a program and the way that partial satisfaction of rules is handled.…”

Section: Introductionmentioning

confidence: 99%

Complexity of fuzzy answer set programming under Łukasiewicz semantics

Blondeel

Schockaert

Vermeir

et al. 2014

International Journal of Approximate Reasoning

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show abstract

“…Our adaptation in the fuzzy stable model semantics is similar to the method from [9], in which the consistency of an interpretation is guaranteed by imposing the extra restriction I(∼p) ≤ ∼I(p) for all atom p. Strong negation and consistency have also been studied in [13,14].…”

Section: Other Related Workmentioning

confidence: 99%

Stable Models of Fuzzy Propositional Formulas

Lee

Wang

2014

Logics in Artificial Intelligence

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Abstract. We introduce the stable model semantics for fuzzy propositional formulas, which generalizes both fuzzy propositional logic and the stable model semantics of Boolean propositional formulas. Combining the advantages of both formalisms, the introduced language allows highly configurable default reasoning involving fuzzy truth values. We show that several properties of Boolean stable models are naturally extended to this formalism, and discuss how it is related to other approaches to combining fuzzy logic and the stable model semantics.

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“…Indeed, many fuzzy reasoning tasks can be reduced to SAT ∞ , including reasoning about vague concepts in the context of the semantic web [4], fuzzy spatial reasoning [5] and fuzzy answer set programming [6], which in itself is an important framework for non-monotonic reasoning over continuous domains (see e.g. [7], [8], [9]). …”

Section: Introductionmentioning

confidence: 99%

Local search and restart strategies for satisfiability solving in fuzzy logics

Brys¹,

Drugan²,

Bosman

et al. 2013

2013 IEEE International Workshop on Genetic and Evolutionary Fuzzy Systems (GEFS)

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Abstract-Satisfiability solving in fuzzy logics is a subject that has not been researched much, certainly compared to satisfiability in propositional logics. Yet, fuzzy logics are a powerful tool for modelling complex problems. Recently, we proposed an optimization approach to solving satisfiability in fuzzy logics and compared the standard Covariance Matrix Adaptation Evolution Strategy algorithm (CMA-ES) with an analytical solver on a set of benchmark problems. Especially on more finegrained problems did CMA-ES compare favourably to the analytical approach. In this paper, we evaluate two types of hillclimber in addition to CMA-ES, as well as restart strategies for these algorithms. Our results show that a population-based hillclimber outperforms CMA-ES on the harder problem class.

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Measuring Inconsistency in Fuzzy Answer Set Semantics

Cited by 36 publications

References 30 publications

Complexity of fuzzy answer set programming under Łukasiewicz semantics

Complexity of fuzzy answer set programming under Łukasiewicz semantics

Stable Models of Fuzzy Propositional Formulas

Local search and restart strategies for satisfiability solving in fuzzy logics

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