Fuzzy answer set computation via satisfiability modulo theories

Author:

ALVIANO MARIO,PEÑALOZA RAFAEL

Abstract

AbstractFuzzy 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.

Publisher

Cambridge University Press (CUP)

Subject

Artificial Intelligence,Computational Theory and Mathematics,Hardware and Architecture,Theoretical Computer Science,Software

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Enhancing and Evaluating the Product Fuzzy DPLL Solver;SN Computer Science;2022-07-21

2. The Implementation of a Product Fuzzy DPLL Solver;Proceedings of the 12th International Joint Conference on Computational Intelligence;2020

3. Fuzzy Answer Set Programming: From Theory to Practice;Studies in Computational Intelligence;2020

4. Foundations of a DPLL-Based Solver for Fuzzy Answer Set Programs;Studies in Computational Intelligence;2019

5. Modeling multi-valued biological interaction networks using fuzzy answer set programming;Fuzzy Sets and Systems;2018-08

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