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An introduction to fuzzy answer set programming

Davy Van Nieuwenborgh, Martine De Cock, Dirk Vermeir
2007 Annals of Mathematics and Artificial Intelligence  
In this paper we show how the concepts of answer set programming and fuzzy logic can be successfully combined into the single framework of fuzzy answer set programming (FASP).  ...  Finally, the presented framework turns out to be a proper extension of classical answer set programming, as we show, in contrast to other proposals in the literature, that there are only minor restrictions  ...  In the fuzzy answer set programming (FASP) framework introduced in this paper, we consider fuzzy answer sets, which means that literals can belong to an answer set to a certain extent, as opposed to either  ... 
doi:10.1007/s10472-007-9080-3 fatcat:dwkwadkwefggznuvowf65paukq

Fuzzy Answer Set Programming: An Introduction [chapter]

Marjon Blondeel, Steven Schockaert, Dirk Vermeir, Martine De Cock
2013 Studies in Fuzziness and Soft Computing  
In this chapter, we present a tutorial about fuzzy answer set programming (FASP); we give a gentle introduction to its basic ideas and definitions.  ...  Despite that very general connectives are allowed, the presented framework turns out to be an intuitive extension of answer set programming.  ...  Introduction In this chapter we will present and illustrate the basic definitions of fuzzy answer set programming (FASP).  ... 
doi:10.1007/978-3-642-34922-5_15 fatcat:sjdl5zq7znfujhvb45zvte4fhe

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  ...  More recently, a general introduction to fuzzy answer set programming has been introduced in [10] , however their approach is not directly applicable to residuated logic programs, since the programs they  ... 
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  
In this chapter, we present a tutorial about fuzzy answer set programming (FASP); we give a gentle introduction to its basic ideas and definitions.  ...  Despite that very general connectives are allowed, the presented framework turns out to be an intuitive extension of answer set programming.  ...  Introduction In this chapter we will present and illustrate the basic definitions of fuzzy answer set programming (FASP).  ... 
doi:10.2991/978-94-91216-59-6_3 fatcat:oqzn4dfxkncd3bs5m3oucm4ahy

Fuzzy Answer Set Programming [chapter]

Davy Van Nieuwenborgh, Martine De Cock, Dirk Vermeir
2006 Lecture Notes in Computer Science  
In this chapter, we present a tutorial about fuzzy answer set programming (FASP); we give a gentle introduction to its basic ideas and definitions.  ...  Despite that very general connectives are allowed, the presented framework turns out to be an intuitive extension of answer set programming.  ...  Introduction In this chapter we will present and illustrate the basic definitions of fuzzy answer set programming (FASP).  ... 
doi:10.1007/11853886_30 fatcat:rp5q3tsbmfb3hblmfalapiq2ce

Logical Fuzzy Preferences [article]

Emad Saad
2013 arXiv   pre-print
We show the application of fuzzy answer set optimization programs to the course scheduling with fuzzy preferences problem.  ...  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.  ...  In addition, we provided an implementation for fuzzy answer set optimization programs in fuzzy answer set programming.  ... 
arXiv:1304.2797v1 fatcat:zifpamspnzex7lqigqrq3fuy6e

Compiling Fuzzy Answer Set Programs to Fuzzy Propositional Theories [chapter]

Jeroen Janssen, Stijn Heymans, Dirk Vermeir, Martine De Cock
2008 Lecture Notes in Computer Science  
We show how a fuzzy answer set program can be compiled to an equivalent fuzzy propositional theory whose models correspond to the answer sets of the program.  ...  This creates a basis for constructing fuzzy answer set solvers, such as solvers based on fuzzy SAT-solvers or on linear programming.  ...  Fuzzy Answer Set Programming Fuzzy answer set programming [3] is an extension of regular answer set programming (see e.g.  ... 
doi:10.1007/978-3-540-89982-2_34 fatcat:2vqqo2pgjngx3nigx4f6wdjlne

Fuzzy logic programming reduced to reasoning with attribute implications

Tomas Kuhr, Vilem Vychodil
2015 Fuzzy sets and systems (Print)  
We present a link between two types of logic systems for reasoning with graded if-then rules: the system of fuzzy logic programming (FLP) in sense of Vojtáš and the system of fuzzy attribute logic (FAL  ...  We show that each finite theory consisting of formulas of FAL can be represented by a definite program so that the semantic entailment in FAL can be characterized by correct answers for the program.  ...  Therefore, by finding fuzzy logic programs corresponding to sets of fuzzy attribute implications, one may introduce an alternative description of fuzzy concept lattices by fuzzy logic programs which we  ... 
doi:10.1016/j.fss.2014.04.013 fatcat:sbr7tegjizc45l45i4en7fcecq

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.  ...  In particular we show that the answer sets of a fuzzy answer set program correspond to the stable expansions of an associated fuzzy autoepistemic logic theory.  ... 
doi:10.1007/978-3-642-22152-1_52 fatcat:kc3crepsknerpm4fienzuxhmne

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

Computing Fuzzy Answer Sets Using dlvhex [chapter]

Davy Van Nieuwenborgh, Martine De Cock, Dirk Vermeir
2007 Lecture Notes in Computer Science  
Fuzzy answer set programming has been introduced as a framework that successfully combines the concepts of answer set programming and fuzzy logic.  ...  In this paper, we show how the fuzzy answer set semantics can be mapped onto the semantics for HEX-programs, which are nonmonotonic logic programs under the answer set semantics that support the use of  ...  From Fuzzy Answer Sets to HEX-programs In this section we present a translation from the FASP semantics to HEX-programs such that the fuzzy answer sets can be retrieved from the answer sets of the HEX-programs  ... 
doi:10.1007/978-3-540-74610-2_40 fatcat:gr3bn4hjojeq7l2prmzrteaaqa

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.  ...  Introduction Fuzzy answer set optimization is a logical framework aims to solve optimization problems in fuzzy environments.  ... 
arXiv:1304.2384v1 fatcat:36wwu35dvjenznjke3wm6zyxeu

Answer Sets in a Fuzzy Equilibrium Logic [chapter]

Steven Schockaert, Jeroen Janssen, Dirk Vermeir, Martine De Cock
2009 Lecture Notes in Computer Science  
Since its introduction, answer set programming has been generalized in many directions, to cater to the needs of real-world applications.  ...  Fuzzy answer set programming, on the other hand, extends answer set programming with the capability of modeling continuous systems.  ...  In practice, an answer set program P , i.e. a set of rules, represents a problem instance, whose solutions correspond to the answer sets of the program.  ... 
doi:10.1007/978-3-642-05082-4_10 fatcat:2icliihgjrggrepgqvz35efhde

Fuzzy Aggregates in Fuzzy Answer Set Programming [article]

Emad Saad
2013 arXiv   pre-print
We show that the proposed fuzzy answer set semantics subsumes both the original fuzzy answer set semantics of DFLP and the classical answer set semantics of classical disjunctive logic programs with classical  ...  Fuzzy answer set programming is a declarative framework for representing and reasoning about knowledge in fuzzy environments.  ...  Introduction Fuzzy answer set programming [Saad, 2010; Saad, 2009; Subrahmanian, 1994 ] is a declarative programming framework that has been shown effective for knowledge representation and reasoning  ... 
arXiv:1304.1827v1 fatcat:k6oggx7kx5cfhnpsasdlzmjh6e

Fuzzy answer sets approximations

MARIO ALVIANO, RAFAEL PEÑALOZA
2013 Theory and Practice of Logic Programming  
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.  ...  To limit this downside, operators for approximating fuzzy answer sets can be introduced: Given a FASP program, these operators compute lower and upper bounds for all atoms in the program such that all  ...  Fuzzy Answer Set Programming (FASP) aims at combining ASP and fuzzy logic.  ... 
doi:10.1017/s1471068413000471 fatcat:fpyawy5gqzfg5d4244sqi5claa
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