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General Fuzzy Answer Set Programs [chapter]

Jeroen Janssen, Steven Schockaert, Dirk Vermeir, Martine De Cock
2009 Lecture Notes in Computer Science  
We introduce a unifying framework that entails most of the existing approaches to fuzzy answer set programming.  ...  A number of generalizations of answer set programming have been proposed in the literature to deal with vagueness, uncertainty, and partial rule satisfaction.  ...  While we have only discussed our framework from a theoretical perspective, we intend to explore the use of expressive fuzzy SAT solvers to find k-answer sets in practice, generalizing a technique proposed  ... 
doi:10.1007/978-3-642-02282-1_44 fatcat:4dtqxxe5hnanpmd4rqszpyf2jq

Logical Fuzzy Preferences [article]

Emad Saad
2013 arXiv   pre-print
We present a unified logical framework for representing and reasoning about both quantitative and qualitative preferences in fuzzy answer set programming, called fuzzy answer set optimization programs.  ...  We show the application of fuzzy answer set optimization programs to the course scheduling with fuzzy preferences problem.  ...  with fuzzy answer set semantics) is used as fuzzy answer sets generator rules.  ... 
arXiv:1304.2797v1 fatcat:zifpamspnzex7lqigqrq3fuy6e

Logical Fuzzy Optimization [article]

Emad Saad
2013 arXiv   pre-print
We present a logical framework to represent and reason about fuzzy optimization problems based on fuzzy answer set optimization programming.  ...  We show the application of the proposed logical fuzzy optimization framework under the fuzzy answer set optimization programming to the fuzzy water allocation optimization problem.  ...  logic program with fuzzy answer set semantics) is used as fuzzy answer sets generator rules.  ... 
arXiv:1304.2384v1 fatcat:36wwu35dvjenznjke3wm6zyxeu

Towards a Fuzzy Answer Set Semantics for Residuated Logic Programs

Nicolás Madrid, Manuel Ojeda-Aciego
2008 2008 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology  
In this work we introduce the first steps towards the definition of an answer set semantics for residuated logic programs with negation.  ...  The definitions of fuzzy stable model for general program and of fuzzy answer set for a coherent normal program are used in order to provide the more general definition of fuzzy answer set for an extended  ...  Therefore, fuzzy logic programming has become a target theory for a suitable generalization of answer set semantics.  ... 
doi:10.1109/wiiat.2008.357 dblp:conf/iat/MadridO08 fatcat:4a4g7hdpuzeerc5l5agj6six54

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.  ...  Despite that very general connectives are allowed, the presented framework turns out to be an intuitive extension of answer set programming.  ...  General programs and answer sets In this section, we will generalize the definitions of ASP to arbitrary FASP programs.  ... 
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.  ...  Despite that very general connectives are allowed, the presented framework turns out to be an intuitive extension of answer set programming.  ...  General programs and answer sets In this section, we will generalize the definitions of ASP to arbitrary FASP programs.  ... 
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.  ...  Despite that very general connectives are allowed, the presented framework turns out to be an intuitive extension of answer set programming.  ...  General programs and answer sets In this section, we will generalize the definitions of ASP to arbitrary FASP programs.  ... 
doi:10.1007/11853886_30 fatcat:rp5q3tsbmfb3hblmfalapiq2ce

Answer Sets in a Fuzzy Equilibrium Logic [chapter]

Steven Schockaert, Jeroen Janssen, Dirk Vermeir, Martine De Cock
2009 Lecture Notes in Computer Science  
Fuzzy answer set programming, on the other hand, extends answer set programming with the capability of modeling continuous systems.  ...  Since its introduction, answer set programming has been generalized in many directions, to cater to the needs of real-world applications.  ...  We can also show that fuzzy equilibrium models generalize the notion of answer set from fuzzy answer set programs to arbitrary sets of fuzzy formulas. Proposition 3.  ... 
doi:10.1007/978-3-642-05082-4_10 fatcat:2icliihgjrggrepgqvz35efhde

Fuzzy Autoepistemic Logic: Reflecting about Knowledge of Truth Degrees [chapter]

Marjon Blondeel, Steven Schockaert, Martine De Cock, Dirk Vermeir
2011 Lecture Notes in Computer Science  
is preserved in the sense that fuzzy autoepistemic logic generalizes fuzzy answer set programming.  ...  Moreover, it is well known to generalize the stable model semantics of answer set programming.  ...  Relation between Fuzzy Answer Set Programming and Fuzzy Autoepistemic Logic Let us briefly recall the basic notion of a fuzzy version of answer set programming, which was recently proposed [10] .  ... 
doi:10.1007/978-3-642-22152-1_52 fatcat:kc3crepsknerpm4fienzuxhmne

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)  
answer set semantics with fuzzy description logics.  ...  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  ...  (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

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

Thomas Lukasiewicz
2006 2006 Second International Conference on Rules and Rule Markup Languages for the Semantic Web (RuleML'06)  
We then define the answer set semantics of general fuzzy dl-programs, and show in particular that all answer sets of a fuzzy dlprogram are minimal models, and that the answer set semantics of positive  ...  In this paper, we present an approach to fuzzy description logic programs under the answer set semantics for the Semantic Web, which is an integration of description logics with nonmonotonic logic programs  ...  General Fuzzy DL-Programs We now define the answer set semantics of general fuzzy dl-programs KB , which is reduced to the least model semantics of positive fuzzy dl-programs.  ... 
doi:10.1109/ruleml.2006.12 dblp:conf/ruleml/Lukasiewicz06 fatcat:qorslyeshzfbhbqol5rclbc6dm

Solving Fuzzy Answer Set Programs in Product Logic

Ivor Uhliarik
2017 Proceedings of the 9th International Joint Conference on Computational Intelligence  
logic, or yield only approximate answer sets.  ...  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  ...  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

On Coherence and Consistence in Fuzzy Answer Set Semantics for Residuated Logic Programs [chapter]

Nicolás Madrid, Manuel Ojeda-Aciego
2009 Lecture Notes in Computer Science  
In this work we recall the first steps towards the definition of an answer set semantics for residuated logic programs with negation, and concentrate on the development of relationships between the notions  ...  Now we are ready to introduce our notion of (fuzzy) answer set for general residuated logic program. Definition 8.  ...  Fuzzy answer sets Once the concept of coherence has been presented, we can introduce the notion of fuzzy answer set for extended logic programs.  ... 
doi:10.1007/978-3-642-02282-1_8 fatcat:hgrbkqsep5e4re4irh2op4jbmu

Fuzzy autoepistemic logic and its relation to fuzzy answer set programming

Marjon Blondeel, Steven Schockaert, Martine De Cock, Dirk Vermeir
2014 Fuzzy sets and systems (Print)  
Moreover, it is well known to generalize the stable model semantics of answer set programming.  ...  We also define a fuzzy logic of minimal belief and negation-as-failure and use this as a tool to show that fuzzy autoepistemic logic generalizes fuzzy answer set programming.  ...  Fuzzy answer set programming (FASP) (e.g.  ... 
doi:10.1016/j.fss.2012.09.012 fatcat:mfbvgiydovesrpruo2v5xn3avu

Ranking Services Using Fuzzy HEX Programs [chapter]

Stijn Heymans, Ioan Toma
2008 Lecture Notes in Computer Science  
In this paper, we generalize both HEX programs and fuzzy dl-programs to fuzzy HEX programs: a LP-based paradigm, supporting both fuzziness as well as reasoning with external sources.  ...  Two functional extensions of dl-programs are HEX programs and fuzzy dl-programs.  ...  Directions for Further Research As future work, we plan to develop a reasoner for fuzzy HEX programs based on the DLVHEX reasoner, using the translation of fuzzy HEX programs to HEX programs presented  ... 
doi:10.1007/978-3-540-88737-9_14 fatcat:yiiktryblfcjbgdgjjnuor2ada
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