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### 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.  ...  FASP is a combination of answer set programming and fuzzy logics which has recently been proposed.  ...  Introduction In this chapter we will present and illustrate the basic definitions of fuzzy answer set programming (FASP).  ...

### 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  ...

### 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.  ...  FASP is a combination of answer set programming and fuzzy logics which has recently been proposed.  ...  Introduction In this chapter we will present and illustrate the basic definitions of fuzzy answer set programming (FASP).  ...

### 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.  ...  FASP is a combination of answer set programming and fuzzy logics which has recently been proposed.  ...  Introduction In this chapter we will present and illustrate the basic definitions of fuzzy answer set programming (FASP).  ...

MARIO ALVIANO, RAFAEL PEÑALOZA
2013 Theory and Practice of Logic Programming
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  ...  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.  ...  Fuzzy Answer Set Programming (FASP) aims at combining ASP and fuzzy logic.  ...

### 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.  ...  As an approximation of full answer sets, k-answer sets are introduced to deal with conflicting information, yielding a flexible framework that encompasses, among others, existing work on valued constraint  ...  to answer set optimization and valued constraint satisfaction.  ...

### Aggregated Fuzzy Answer Set Programming

Jeroen Janssen, Steven Schockaert, Dirk Vermeir, Martine De Cock
2011 Annals of Mathematics and Artificial Intelligence
Fuzzy Answer Set programming (FASP) is an extension of answer set programming (ASP), based on fuzzy logic.  ...  In this paper, we develop an alternative, based on aggregator functions that specify which (combination of) rules are most important to satisfy.  ...  Fuzzy Answer Set Programming In [80] , Fuzzy Answer Set Programming is introduced.  ...

### Aggregated 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
Fuzzy Answer Set programming (FASP) is an extension of answer set programming (ASP), based on fuzzy logic.  ...  In this paper, we develop an alternative, based on aggregator functions that specify which (combination of) rules are most important to satisfy.  ...  Fuzzy Answer Set Programming In [80] , Fuzzy Answer Set Programming is introduced.  ...

### Fuzzy Aggregates in Fuzzy Answer Set Programming [article]

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  ...

### 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.  ...  Introduction Answer Set Programming (ASP) is one of the most popular and well-studied declarative programming paradigms [2, 11] .  ...

### 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.  ...

### 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.  ...

### 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.  ...  Introduction Answer Set Programming (ASP), see e.g. (Baral 2003 ) is a form of non-monotonic reasoning based on the stable model semantics for logic programming (Gelfond and Lifschitz 1988) .  ...

### 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)
In this paper, we consider a version of fuzzy answer set programming and show that its answer sets can be equivalently described as models in fuzzy autoepistemic logic.  ...  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.  ...  Introduction Answer set programming (ASP) is a tool for modeling combinatorial search problems in a declarative way [1] .  ...

### 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
A well-known technique for classical ASP consists of translating an ASP program P to a propositional theory whose models exactly correspond to the answer sets of P.  ...  In recent years answer set programming has been extended to deal with multi-valued predicates.  ...  Introduction Answer Set Programming (ASP), see e.g. (Baral 2003 ) is a form of non-monotonic reasoning based on the stable model semantics for logic programming (Gelfond and Lifschitz 1988) .  ...
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