Stable Models of Fuzzy Propositional Formulas

Lee, Joohyung; Wang, Yi

doi:10.1007/978-3-319-11558-0_23

Cited by 4 publications

(5 citation statements)

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“…Fuzzy Answer Set Programming (FASP) (Nieuwenborgh, Cock, and Vermeir 2007;Janssen et al 2012a;2012b;Blondeel et al 2013;Lee and Wang 2014;Mushthofa, Schockaert, and Cock 2015) is a successfully combination of Fuzzy Logic (Cintula, Hájek, and Noguera 2011) and Answer Set Programming (ASP) (Gelfond and Lifschitz 1991;Marek and Truszczyński 1999;Niemelä 1999), which resulted in a declarative framework supporting non-monotonic reasoning on propositional formulas interpreted by truth degrees in the interval [0, 1]. As in ASP, reasoning on unknown knowledge is eased by the use of default negation, whose semantics is elegantly captured by the notion of answer set, or stable model: in a model, truth of unknown knowledge may be assumed as soon as there is no evidence of the contrary, and the model is discarded when the truth of some propositions is not necessary in order to satisfy the input program under the assumption for the unknown knowledge provided by the model itself.…”

Section: Introductionmentioning

confidence: 99%

Minimal Undefinedness for Fuzzy Answer Sets

Alviano

Amendola

Peñaloza

2017

AAAI

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Fuzzy Answer Set Programming (FASP) combines the non-monotonic reasoning typical of Answer Set Programming with the capability of Fuzzy Logic to deal with imprecise information and paraconsistent reasoning. In the context of paraconsistent reasoning, the fundamental principle of minimal undefinedness states that truth degrees close to 0 and 1 should be preferred to those close to 0.5, to minimize the ambiguity of the scenario. The aim of this paper is to enforce such a principle in FASP through the minimization of a measure of undefinedness. Algorithms that minimize undefinedness of fuzzy answer sets are presented, and implemented.

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Section: Introductionmentioning

confidence: 99%

Minimal Undefinedness for Fuzzy Answer Sets

Alviano

Amendola

Peñaloza

2017

AAAI

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“…Intuitively, the higher the degree assigned to a proposition, the more true it is, with 0 and 1 denoting totally false and totally true, respectively. The notion of fuzzy answer set, or fuzzy stable model, was recently extended to arbitrary propositional formulas (Lee and Wang 2014). Lee and Wang also propose an example on modeling dynamic trust in social networks, which inspired the following simplified scenario that clarifies how truth degrees increase the knowledge representation capability of ASP.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, ffasp tests by default a limited set of values. Neither fasp nor ffasp accept nesting of negation, which would allow to encode choice rules, a convenient way for guessing truth degrees without using auxiliary atoms (Lee and Wang 2014). Indeed, choice rules allow to check satisfiability of fuzzy propositional formulas without adding new atomic propositions.…”

Section: Introductionmentioning

confidence: 99%

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Fuzzy answer set computation via satisfiability modulo theories

Alviano

Peñaloza

2015

Theory and Practice of Logic Programming

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Fuzzy answer set programming (FASP) combines two declarative frameworks, answer set programming and fuzzy logic, in order to model reasoning by default over imprecise information. Several connectives are available to combine different expressions; in particular the Gödel and Lukasiewicz fuzzy connectives are usually considered, due to their properties. Although the Gödel conjunction can be easily eliminated from rule heads, we show through complexity arguments that such a simplification is infeasible in general for all other connectives. The paper analyzes a translation of FASP programs into satisfiability modulo theories (SMT), which in general produces quantified formulas because of the minimality of the semantics. Structural properties of many FASP programs allow to eliminate the quantification, or to sensibly reduce the number of quantified variables. Indeed, integrality constraints can replace recursive rules commonly used to force Boolean interpretations, and completion subformulas can guarantee minimality for acyclic programs with atomic heads. Moreover, head cycle free rules can be replaced by shifted subprograms, whose structure depends on the eliminated head connective, so that ordered completion may replace the minimality check if also Lukasiewicz disjunction in rule bodies is acyclic. The paper also presents and evaluates a prototype system implementing these translations.

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“…However, most of the work is limited to simple rules. In our previous work (Lee and Wang 2014), we proposed a stable model semantics for fuzzy propositional formulas, which properly generalizes both fuzzy logic and the Boolean stable model semantics, as well as many existing approaches to combining them. The resulting language combines the many-valued nature of fuzzy logic and the nonmonotonicity of stable model semantics, and consequently shows competence in commonsense reasoning involving fuzzy values.…”

Section: Introductionmentioning

confidence: 99%