Let L be a finite distributive lattice and µ : L → R+ a logsupermodular function. For functions k : L → R+ let Eµ(k; q) def = x∈L k(x)µ(x)qrank(x) ∈ R+ [q]. We prove fo...
A residuated algebra (RA) is a generalization of a residuated groupoid; instead of one basic binary operation · with residual operations \, /, it admits finitely many basic oper...
A D-polyhedron is a polyhedron P such that if x, y are in P then so are their componentwise max and min. In other words, the point set of a D-polyhedron forms a distributive latti...
We study the problem of reasoning over weighted ontologies. We assume that every axiom is labeled with an element of a distributive lattice (called its weight) and try to compute i...
Representing and reasoning with an agent's preferences is important in many applications of constraints formalisms. Such preferences are often only partially ordered. One clas...
Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. The homomorphicity order of k-posets is shown to be a distributive lattice. Homomorph...
This paper constructs a logic of soft constraints where the set of degrees of preference forms a partially ordered set. When the partially ordered set is a distributive lattice, th...