Soft Constraints Processing over Divisible Residuated Lattices

Authors:
Simone Bova
Affiliations:
Department of Computer Science, University of Milan, Milan, Italy 20135
Venue:
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Year:
2009

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Abstract

We claim that divisible residuated lattices (DRLs) can act as a unifying evaluation framework for soft constraint satisfaction problems (soft CSPs). DRLs form the algebraic semantics of a large family of substructural and fuzzy logics [13,15], and are therefore natural candidates for this role. As a preliminary evidence in support to our claim, along the lines of Cooper et al. and Larrosa et al. [11,18], we describe a polynomial-time algorithm that enforces k -hyperarc consistency on soft CSPs evaluated over DRLs. Observed that, in general, DRLs are neither idempotent nor totally ordered, this algorithm accounts as a generalization of available enforcing algorithms over commutative idempotent semirings and fair valuation structures [4,11].