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Fuzzy answer set computation via satisfiability modulo theories

Published online by Cambridge University Press:  03 September 2015

MARIO ALVIANO  and
RAFAEL PEÑALOZA
MARIO ALVIANO
Affiliation:
University of Calabria, Italy
RAFAEL PEÑALOZA
Affiliation:
Free University of Bozen-Bolzano, Italy
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Abstract

Fuzzy answer set programming (FASP) combines two declarative frameworks, answer set programming and fuzzy logic, in order to model reasoning by default over imprecise information. Several connectives are available to combine different expressions; in particular the Gödel and Łukasiewicz fuzzy connectives are usually considered, due to their properties. Although the Gödel conjunction can be easily eliminated from rule heads, we show through complexity arguments that such a simplification is infeasible in general for all other connectives. The paper analyzes a translation of FASP programs into satisfiability modulo theories (SMT), which in general produces quantified formulas because of the minimality of the semantics. Structural properties of many FASP programs allow to eliminate the quantification, or to sensibly reduce the number of quantified variables. Indeed, integrality constraints can replace recursive rules commonly used to force Boolean interpretations, and completion subformulas can guarantee minimality for acyclic programs with atomic heads. Moreover, head cycle free rules can be replaced by shifted subprograms, whose structure depends on the eliminated head connective, so that ordered completion may replace the minimality check if also Łukasiewicz disjunction in rule bodies is acyclic. The paper also presents and evaluates a prototype system implementing these translations.

Keywords

answer set programmingfuzzy logicsatisfiability modulo theories
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 15 , Special Issue 4-5: 31st International Conference on Logic Programming , July 2015 , pp. 588 - 603
Copyright
Copyright © Cambridge University Press 2015 

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