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Fuzzy answer sets approximations

Published online by Cambridge University Press:  25 September 2013

MARIO ALVIANO  and
RAFAEL PEÑALOZA
MARIO ALVIANO
Affiliation:
Department of Mathematics and Computer Science, University of Calabria, 87036 Rende (CS), Italy (e-mail: alviano@mat.unical.it)
RAFAEL PEÑALOZA
Affiliation:
Dresden University of Technology, 01062 Dresden, GermanyCenter for Advancing Electronics Dresden (e-mail: penaloza@tcs.inf.tu-dresden.de)
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Abstract

Fuzzy 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 now, no implementations of FASP solvers are available and all current proposals are based on compilations of logic programs into different paradigms, like mixed integer programs or bilevel programs. These approaches introduce many auxiliary variables which might affect the performance of a solver negatively. 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 answer sets are between these bounds. This paper analyzes several operators of this kind which are based on linear programming, fuzzy unfounded sets and source pointers. Furthermore, the paper reports on a prototypical implementation, also describing strategies for avoiding computations of these operators when they are guaranteed to not improve current bounds. The operators and their implementation can be used to obtain more constrained mixed integer or bilevel programs, or even for providing a basis for implementing a native FASP solver. 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 need for an external tool.

Keywords

fuzzy logicanswer set programmingsearch-space pruning operators
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 13 , Special Issue 4-5: 29th International Conference on Logic Programming , July 2013 , pp. 753 - 767
Copyright
Copyright © 2013 [MARIO ALVIANO and RAFAEL PEÑALOZA] 

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Footnotes

*

Partially supported by Regione Calabria within the PIA project KnowRex POR FESR 2007–2013.

†

Partially supported by DFG under grant BA 1122/17-1 and within the Cluster of Excellence ‘cfAED’.

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