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Complexity of fuzzy answer set programming under Łukasiewicz semantics

Marjon Blondeel, Steven Schockaert, Dirk Vermeir, Martine De Cock
2014 International Journal of Approximate Reasoning  
In this paper, we analyze the computational 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.  ... 
doi:10.1016/j.ijar.2013.10.011 fatcat:6w76t2lnafbnxpi2gex7mnsg3y

Tightly Coupled Fuzzy Description Logic Programs under the Answer Set Semantics for the Semantic Web

Thomas Lukasiewicz, Umberto Straccia
2008 International Journal on Semantic Web and Information Systems (IJSWIS)  
We present a novel approach to 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 .  ... 
doi:10.4018/jswis.2008070104 fatcat:ywk4xuriyjg7nld7qpbfbbd7fi

Solving Fuzzy Answer Set Programs in Product Logic

Ivor Uhliarik
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.  ... 
doi:10.5220/0006518303670372 dblp:conf/ijcci/Uhliarik17 fatcat:h5soko66cnhcxeupg6g4sro75q

Fuzzy answer sets approximations

MARIO ALVIANO, RAFAEL PEÑALOZA
2013 Theory and Practice of Logic Programming  
Interestingly, the 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  ... 
doi:10.1017/s1471068413000471 fatcat:fpyawy5gqzfg5d4244sqi5claa

Fuzzy Answer Set Programming [chapter]

Jeroen Janssen, Steven Schockaert, Dirk Vermeir, Martine de Cock
2012 Answer Set Programming for Continuous Domains: A Fuzzy Logic Approach  
FASP is a combination 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.  ... 
doi:10.2991/978-94-91216-59-6_3 fatcat:oqzn4dfxkncd3bs5m3oucm4ahy

Fuzzy Answer Set Programming: An Introduction [chapter]

Marjon Blondeel, Steven Schockaert, Dirk Vermeir, Martine De Cock
2013 Studies in Fuzziness and Soft Computing  
FASP is a combination 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.  ... 
doi:10.1007/978-3-642-34922-5_15 fatcat:sjdl5zq7znfujhvb45zvte4fhe

Fuzzy Answer Set Programming [chapter]

Davy Van Nieuwenborgh, Martine De Cock, Dirk Vermeir
2006 Lecture Notes in Computer Science  
FASP is a combination 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.  ... 
doi:10.1007/11853886_30 fatcat:rp5q3tsbmfb3hblmfalapiq2ce

On the Semantic Relationship between Probabilistic Soft Logic and Markov Logic [article]

Joohyung Lee, Yi Wang
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.  ... 
arXiv:1606.08896v1 fatcat:e2cfanjipraydkacie62ifcz4a

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

Umberto Straccia
2011 Lecture Notes in Computer Science  
This talk presents a detailed, self-contained and comprehensive account 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  ... 
doi:10.1007/978-3-642-23963-2_2 fatcat:vwgiptrpena7dkckythul4tke4

Uncertainty Reasoning for the Semantic Web [chapter]

Thomas Lukasiewicz
2009 Lecture Notes in Computer Science  
., brave) consequence 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.  ... 
doi:10.1007/978-3-642-05082-4_3 fatcat:ojaedt2s6jc2jmocn2ie2ewejy

Uncertainty Reasoning for the Semantic Web [chapter]

Thomas Lukasiewicz
2017 Lecture Notes in Computer Science  
., brave) consequence 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.  ... 
doi:10.1007/978-3-319-61033-7_8 fatcat:hszvhxxiind3pjxrw6d6rnmmse

Reducing Fuzzy Answer Set Programming to Model Finding in Fuzzy Logics [article]

Jeroen Janssen, Steven Schockaert, Dirk Vermeir, Martine De Cock
2011 arXiv   pre-print
However, contrary to the case 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;  ... 
arXiv:1104.5133v1 fatcat:aksfbu2tnzgntbwub465in7xhy

Reducing fuzzy answer set programming to model finding in fuzzy logics

JEROEN JANSSEN, DIRK VERMEIR, STEVEN SCHOCKAERT, MARTINE DE COCK
2011 Theory and Practice of Logic Programming  
AbstractIn recent years, 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;  ... 
doi:10.1017/s1471068411000093 fatcat:unnwhgj5ejgyvihdh2oe3l6ibq

Solving Disjunctive Fuzzy Answer Set Programs [chapter]

Mushthofa Mushthofa, Steven Schockaert, Martine De Cock
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.  ... 
doi:10.1007/978-3-319-23264-5_38 fatcat:ctsq7oizejfblcln2ceywqiwem

From Fuzzy to Annotated Semantic Web Languages [chapter]

Umberto Straccia, Fernando Bobillo
2017 Lecture Notes in Computer Science  
We present the state 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.  ... 
doi:10.1007/978-3-319-49493-7_6 fatcat:u4kbfmvkmbhiberrhh4bocml6u
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