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Complexity of fuzzy answer set programming under Łukasiewicz semantics

2014
*
International Journal of Approximate Reasoning
*

In this paper, we analyze the computational

doi:10.1016/j.ijar.2013.10.011
fatcat:6w76t2lnafbnxpi2gex7mnsg3y
*complexity**of*FASP*under**Lukasiewicz**semantics*. ...*Fuzzy**answer**set**programming*(FASP) is a generalization*of**answer**set**programming*(ASP) in which propositions are allowed to be graded. ... Conclusions In this paper, we presented an overview about the computational*complexity**of*FASP*under**Lukasiewicz**semantics*. ...##
###
Tightly Coupled Fuzzy Description Logic Programs under the Answer Set Semantics for the Semantic Web

2008
*
International Journal on Semantic Web and Information Systems (IJSWIS)
*

We present a novel approach to

doi:10.4018/jswis.2008070104
fatcat:ywk4xuriyjg7nld7qpbfbbd7fi
*fuzzy*description logic*programs*(or simply*fuzzy*dl-*programs*)*under*the*answer**set**semantics*, which is a tight integration*of**fuzzy*disjunctive logic*programs**under*the ...*answer**set**semantics*with*fuzzy*description logics. ... (a) Let I ⊆ HB Φ be any*answer**set**of*KB . That is, I is a minimal model*of*KB I = (L, P I ). In particular, (i) I |= L and (ii) I |= r for every r ∈ P I . ...##
###
Solving Fuzzy Answer Set Programs in Product Logic

2017
*
Proceedings of the 9th International Joint Conference on Computational Intelligence
*

*Fuzzy*

*answer*

*set*

*programming*(FASP) has emerged as a combination

*of*a tool for non-monotonic reasoning and solving combinatorial problems (ASP) and a knowledge representation formalism that allows for ... logic, or yield only approximate

*answer*

*sets*. ...

*FUZZY*

*ANSWER*

*SET*

*PROGRAMMING*In this section we describe the syntax and

*semantics*

*of*

*fuzzy*

*answer*

*set*

*programs*. ...

##
###
Fuzzy answer sets approximations

2013
*
Theory and Practice of Logic Programming
*

Interestingly, the

doi:10.1017/s1471068413000471
fatcat:fpyawy5gqzfg5d4244sqi5claa
*semantics**of*relevant classes*of**programs*with unique*answer**sets*, like positive*programs*and*programs*with stratified negation, can be already computed by the prototype without the ... AbstractFuzzy*answer**set**programming*(FASP) is a recent formalism for knowledge representation that enriches the declarativity*of**answer**set**programming*by allowing propositions to be graded. ... Introduction*Answer**Set**Programming*(ASP), i.e., logic*programming**under*stable model*semantics*(Gelfond and Lifschitz 1991) , is a declarative language for knowledge representation (Niemelä 1999; Marek ...##
###
Fuzzy Answer Set Programming
[chapter]

2012
*
Answer Set Programming for Continuous Domains: A Fuzzy Logic Approach
*

FASP is a combination

doi:10.2991/978-94-91216-59-6_3
fatcat:oqzn4dfxkncd3bs5m3oucm4ahy
*of**answer**set**programming*and*fuzzy*logics which has recently been proposed. ... From the*answer**set**semantics*, FASP inherits the declarative nonmonotonic reasoning capabilities, while*fuzzy*logic adds the power to model continuous problems. ... In [4] some results about the computational*complexity**of*FASP with*Łukasiewicz**semantics*are presented. ...##
###
Fuzzy Answer Set Programming: An Introduction
[chapter]

2013
*
Studies in Fuzziness and Soft Computing
*

FASP is a combination

doi:10.1007/978-3-642-34922-5_15
fatcat:sjdl5zq7znfujhvb45zvte4fhe
*of**answer**set**programming*and*fuzzy*logics which has recently been proposed. ... From the*answer**set**semantics*, FASP inherits the declarative nonmonotonic reasoning capabilities, while*fuzzy*logic adds the power to model continuous problems. ... In [4] some results about the computational*complexity**of*FASP with*Łukasiewicz**semantics*are presented. ...##
###
Fuzzy Answer Set Programming
[chapter]

2006
*
Lecture Notes in Computer Science
*

FASP is a combination

doi:10.1007/11853886_30
fatcat:rp5q3tsbmfb3hblmfalapiq2ce
*of**answer**set**programming*and*fuzzy*logics which has recently been proposed. ... From the*answer**set**semantics*, FASP inherits the declarative nonmonotonic reasoning capabilities, while*fuzzy*logic adds the power to model continuous problems. ... In [4] some results about the computational*complexity**of*FASP with*Łukasiewicz**semantics*are presented. ...##
###
On the Semantic Relationship between Probabilistic Soft Logic and Markov Logic
[article]

2016
*
arXiv
*
pre-print

*of*the weight scheme

*of*MLN for the many-valued

*setting*. ... This is facilitated by first extending

*fuzzy*logic to allow weights, which can be also viewed as a generalization

*of*PSL, and then relate that generalization to MLN. ... This work was partially supported by the National Science Foundation

*under*Grants IIS-1319794, IIS-1526301, and a gift funding from Robert Bosch LLC. ...

##
###
Fuzzy Logic, Annotation Domains and Semantic Web Languages
[chapter]

2011
*
Lecture Notes in Computer Science
*

This talk presents a detailed, self-contained and comprehensive account

doi:10.1007/978-3-642-23963-2_2
fatcat:vwgiptrpena7dkckythul4tke4
*of*the state*of*the art in representing and reasoning with*fuzzy*knowledge in*Semantic*Web Languages such a RDF/RDFS, OWL 2 and RIF ... Basically [43] , a Datalog*program*P is made out by a*set**of*rules and a*set**of*facts. Facts are ground atoms*of*the form P (c). ... For instance, the*fuzzy*GCI in Eq. (10), can be expressed easily as the*fuzzy*rule A*fuzzy*query is a*fuzzy*rule and, informally, the*fuzzy**answer**set*is the ordered*set**of*weighted tuples t, s such that ...##
###
Uncertainty Reasoning for the Semantic Web
[chapter]

2009
*
Lecture Notes in Computer Science
*

., brave) consequence

doi:10.1007/978-3-642-05082-4_3
fatcat:ojaedt2s6jc2jmocn2ie2ewejy
*of*a disjunctive dl-*program*KB*under*the*answer**set**semantics*iff every (resp., some)*answer**set**of*KB satisfies a. ... The*answer**set**semantics**of*disjunctive dl-*programs*faithfully extends its ordinary counterpart and the first-order*semantics**of*description logic knowledge bases. ...##
###
Uncertainty Reasoning for the Semantic Web
[chapter]

2017
*
Lecture Notes in Computer Science
*

., brave) consequence

doi:10.1007/978-3-319-61033-7_8
fatcat:hszvhxxiind3pjxrw6d6rnmmse
*of*a disjunctive dl-*program*KB*under*the*answer**set**semantics*iff every (resp., some)*answer**set**of*KB satisfies a. ... The*answer**set**semantics**of*disjunctive dl-*programs*faithfully extends its ordinary counterpart and the first-order*semantics**of*description logic knowledge bases. ...##
###
Reducing Fuzzy Answer Set Programming to Model Finding in Fuzzy Logics
[article]

2011
*
arXiv
*
pre-print

However, contrary to the case

arXiv:1104.5133v1
fatcat:aksfbu2tnzgntbwub465in7xhy
*of*classical ASP where many efficient solvers have been constructed, to date there is no efficient*fuzzy**answer**set**programming*solver. ... In recent years*answer**set**programming*has been extended to deal with multi-valued predicates. ...*Fuzzy**Answer**Set**Programming*Over the years many different*fuzzy**answer**set**programming*formalisms have been developed (*Lukasiewicz*2006;*Lukasiewicz*and Straccia 2007a; Madrid and Ojeda-Aciego 2008; ...##
###
Reducing fuzzy answer set programming to model finding in fuzzy logics

2011
*
Theory and Practice of Logic Programming
*

AbstractIn recent years,

doi:10.1017/s1471068411000093
fatcat:unnwhgj5ejgyvihdh2oe3l6ibq
*answer**set**programming*(ASP) has been extended to deal with multivalued predicates. ... A well-knowntechnique for classical ASP consists*of*translating an ASP programPto a propositional theory whose models exactlycorrespond to the*answer**sets*ofP. ...*Fuzzy**Answer**Set**Programming*Over the years many different*fuzzy**answer**set**programming*formalisms have been developed (*Lukasiewicz*2006;*Lukasiewicz*and Straccia 2007a; Madrid and Ojeda-Aciego 2008; ...##
###
Solving Disjunctive Fuzzy Answer Set Programs
[chapter]

2015
*
Lecture Notes in Computer Science
*

*Fuzzy*

*Answer*

*Set*

*Programming*(FASP) is an extension

*of*the popular

*Answer*

*Set*

*Programming*(ASP) paradigm which is tailored for continuous domains. ... We first show that a large class

*of*disjunctive FASP

*programs*called the self-reinforcing cycle-free (SRCF)

*programs*can be polynomially reduced to normal FASP

*programs*. ... In [5] , the

*complexity*

*of*

*answer*

*set*existence,

*set*-membership and

*set*-entailment in various classes

*of*FASP

*under*the

*Łukasiewicz*

*semantics*was studied. ...

##
###
From Fuzzy to Annotated Semantic Web Languages
[chapter]

2017
*
Lecture Notes in Computer Science
*

We present the state

doi:10.1007/978-3-319-49493-7_6
fatcat:u4kbfmvkmbhiberrhh4bocml6u
*of*the art in representing and reasoning with*fuzzy*knowledge in*Semantic*Web Languages such as triple languages RDF/RDFS, conceptual languages*of*the OWL 2 family and rule languages ... Capturing Intelligence:*Fuzzy*Logic and the*Semantic*Web. Elsevier, Amsterdam (2006) 48.*Lukasiewicz*, T.:*Fuzzy*description logic*programs**under*the*answer**set**semantics*for the*semantic*web. ...*Lukasiewicz*, T.:*Fuzzy*description logic*programs**under*the*answer**set**semantics*forthe*semantic*web. Fundamenta Informaticae 82(3), 289-310 (2008) Table 1 . 1 Properties for t-norms and s-norms. ...
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