Soft Constraints Processing over Divisible Residuated Lattices

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].