An introduction to fuzzy answer set programming

Abstract

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). The framework offers the best of both worlds: from the answer set semantics, it inherits the truly declarative non-monotonic reasoning capabilities while, on the other hand, the notions from fuzzy logic in the framework allow it to step away from the sharp principles used in classical logic, e.g., that something is either completely true or completely false. As fuzzy logic gives the user great flexibility regarding the choice for the interpretation of the notions of negation, conjunction, disjunction and implication, the FASP framework is highly configurable and can, e.g., be tailored to any specific area of application. 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 one has to demand on the fuzzy operations used, in order to be able to retrieve the classical semantics using FASP.

Fuzzy Answer Set Programming: An Introduction

“…the set of literals in P and to add the rules 1 ← a ⊕ ¬a for each a ∈ L P . In [21], degrees of consistency of fuzzy interpretations are discussed.…”

“…In recent years a variety of approaches to FASP have been Marjon Blondeel Vrije Universiteit Brussel, Department of Computer Science, Pleinlaan 2, 1050 Brussel, Belgium, e-mail: mblondee@vub.ac.be proposed (e.g. [5], [10], [12], [21]). This framework is a generalization of answer set programming using fuzzy logics, a class of logics whose semantics are based on truth values taken from the unit interval [0, 1] [9].…”

Computing Fuzzy Answer Sets Using dlvhex

“…In [18,17] both formalisms, i.e. ASP and fuzzy logic, have been combined into the single framework of fuzzy answer set programming (FASP) to increase the flexibility and hence the application potential of ASP.…”

“…Similarly, a more flexible interpretation of negation as failure is allowed and a rule can be satisfied to a certain degree. While [18] defines the semantics in a direct fashion, similar to the normal ASP semantics, [17] adapts the notion of an unfounded set to the setting of fuzzy interpretations.…”

“…The mapping we propose in this work to compute fuzzy answer sets using HEXprograms is based on the characterisation of the FASP semantics with unfounded sets from [17]. The idea behind the mapping comes from the guess-and-check methodology that is often used in ASP applications.…”