In the lattice theory the tensor product A⊗B is naturally defined on (0,∨)−semilattices. In general, when restricted to lattices this construction will not yield a lattice. However, if the tensor product A ⊗ B is capped, then A⊗B is a lattice. It is stated as an open problem in [4] whether the converse is true. In the present paper we prove that it is not so, that is, there are bounded lattices...

Benado (Čehoslovak.Mat. Ž. 79(4) (1954) 105–129) and later Hansen (DiscreteMath. 33(1) (1981) 99–101) have offered an algebraic characterization of multilattice (i.e., a poset where every pair of elements satisfies that any upper bound is greater than or equal to a minimal upper bound, and also satisfies the dual property). To that end, they introduce two algebraic operators that are a generali...

In their 1936 seminal paper, Birkhoff and von Neumann made the proposal of a non-classical logic for quantum mechanics founded on the basic lattice-order properties of all closed subspaces of a Hilbert space. These lattice-order properties are captured in the orthomodular lattice structure, characterized by a weak form of distributivity called orthomodular law. This “weak distributivity”, which...

A new class of operator algebras, Kadison-Singer algebras (KS-algebras), is introduced. These highly noncommutative, non-self-adjoint algebras generalize triangular matrix algebras. They are determined by certain minimally generating lattices of projections in the von Neumann algebras corresponding to the commutant of the diagonals of the KS-algebras. A new invariant for the lattices is introdu...

For a given complete lattice L, we investigate whether L can be decomposed as a direct product of directly indecomposable lattices. We prove that this is the case if every element of L is a join of join-irreducible elements and dually, thus extending to non-algebraic lattices a result of L. Libkin. We illustrate this by various examples and counterexamples.

In this paper we show that there is a correspondence between some K3 surfaces with non-isometric transcendental lattices constructed as a twist of the transcendental lattice of the Jacobian of a generic genus 2 curve. Moreover, we show the existence of a correspondence between a general K3 surface with ρ = 17 and a Kummer surface having transcendental lattices Q-Hodge isomorphic.

We present a simple, yet general top-down query answering procedure for normal logic programs over lattices and bilattices, where functions may appear in the rule bodies. Its interest relies on the fact that many approaches to paraconsistency and uncertainty in logic programs with or without non-monotonic negation are based on bilattices or lattices, respectively.

In general frequent itemsets are generated from large data sets by applying various association rule mining algorithms, these produce many redundant frequent itemsets. In this paper we proposed a new framework for Non-redundant frequent itemset generation using closed frequent itemsets without lose of information on Taxonomy Datasets using concept lattices. General Terms Frequent Pattern, Assoc...