可除剩余格上软约束的k-超弧一致性
k-Hyperarc Consistency for Soft Constraints over Divisible Residuated Lattices
摘要：
我们研究了可分剩余格（DRL）作为软约束满足问题（软CSP）的一般评价框架的适用性。DRL实际上是这个角色的自然候选者，因为它们形成了一个大家族的子结构和模糊逻辑的代数语义。我们提出以下结果。(i)我们表明，DRL subterranial重要的软约束，如交换幂等半环和公平的估值结构的估值结构，在这个意义上说，最后两个是成员的某些子品种的DRL（即，Heyting代数和BL-代数分别）。(ii)在J. Larrosa和T. Schiex [2004]和S. Bistarelli和F. Gadducci [2006]描述了一种多项式时间算法，该算法在DRL上评估的软CSP上强制执行k-超弧一致性。观察到，在一般情况下，DRL既不是幂等的，也不是完全有序的，该算法的可用算法，强制执行k-超弧一致性的推广。
英文摘要：
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.
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