  We investigate the applicability of divisible residuated lattices (DRLs) as a
general evaluation framework for soft constraint satisfaction problems (soft
CSPs). DRLs are in fact natural candidates for this role, since they form the
algebraic semantics of a large family of substructural and fuzzy logics.
  We present the following results. (i) We show that DRLs subsume important
valuation structures for soft constraints, such as commutative idempotent
semirings and fair valuation structures, in the sense that the last two are
members of certain subvarieties of DRLs (namely, Heyting algebras and
BL-algebras respectively). (ii) In the spirit of previous work of J. Larrosa
and T. Schiex [2004], and S. Bistarelli and F. Gadducci [2006] 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 amounts to a generalization of the available
algorithms that enforce k-hyperarc consistency.
