We show that a locally finite variety which omits abelian types is self–rectangulating if and only if it has a compatible semilattice term operation. Such varieties must have type–set {5 }. These varieties are residually small and, when they are finitely generated, they have definable principal congruences. We show that idempotent varieties with a compatible semilattice term operation have the ...

We define the tensor product A ® S for arbitrary semilattices A and B. The construction is analogous to one used in ring theory (see 14], [7], [8]) and different from one studied by A. Waterman [12], D. Mowat [9], and Z. Shmuely [10]. We show that the semilattice A <3 B is a distributive lattice whenever A and B are distributive lattices, and we investigate the relationship between the Stone sp...

A specialization semilattice is a join together with coarser preorder $ \sqsubseteq satisfying an appropriate compatibility condition. If $X$ topological space, then $(\mathcal P(X), \cup, )$ semilattice, where x y$ if $x \subseteq Ky$, for $x,y X$, and $K$ closure. Specialization semilattices posets appear as auxiliary structures in many disparate scientific fields, even unrelated to topology....

In this paper, we study structures such as distributive lattices, semilattices, and median graphs from an algorithmic point of view. Such are very useful in classification phylogeny for representing lineage relationships example. A lattice can be considered a graph while ∨-semilattice provided that some conditions holding on triple elements satisfied. Starting structure with different represent...

The aim of this work is the formalization of Chapter 0 Section 4 of [11]. In this paper the definition of meet-continuous lattices is introduced. Theorem 4.2 and Remark 4.3 are proved. Let X, Y be non empty sets, let f be a function from X into Y , and let Z be a non empty subset of X. One can verify that f • Z is non empty. Let us note that every non empty relational structure which is reflexi...

Tracing back from Charnes, Cooper and Rhodes [9] many approaches have been proposed to extend the DEA production model to non-convex technologies. The FDH method were introduced by Deprins, Simar and Tulkens [13] and it only assumes a free disposal assumption of the technology. This paper, continues further an earlier work by Briec and Horvath [7]. Among other things, a new class of semilattice...

Let S, T be semilattices. Let us assume that if S is upper-bounded, then T is upper-bounded. A map from S into T is said to be a semilattice morphism from S into T if: (Def. 1) For every finite subset X of S holds it preserves inf of X. Let S, T be semilattices. One can check that every map from S into T which is meet-preserving is also monotone. Let S be a semilattice and let T be an upper-bou...

The semilattice relevant logics ∪R, ∪T, ∪RW, and ∪TW (slightly different from the orthodox relevant logics R, T, RW, and TW) are defined by “semilattice models” in which conjunction and disjunction are interpreted in a natural way. In this paper, we prove the equivalence between “LK-style” and “LJ-style” labelled sequent calculi for these logics. (LKstyle sequents have plural succedents, while ...