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On the construction of dense lattices with a given automorphisms group

Philippe Gaborit, Gilles Zémor (2007)

Annales de l’institut Fourier

We consider the problem of constructing dense lattices in ℝ n with a given non trivial automorphisms group. We exhibit a family of such lattices of density at least c n 2 - n , which matches, up to a multiplicative constant, the best known density of a lattice packing. For an infinite sequence of dimensions n , we exhibit a finite set of lattices that come with an automorphisms group of size n , and a constant proportion of which achieves the aforementioned lower bound on the largest packing density. The algorithmic...

Poset-valued preference relations

Vladimír Janiš, Susana Montes, Branimir Šešelja, Andreja Tepavčević (2015)

Kybernetika

In decision processes some objects may not be comparable with respect to a preference relation, especially if several criteria are considered. To provide a model for such cases a poset valued preference relation is introduced as a fuzzy relation on a set of alternatives with membership values in a partially ordered set. We analyze its properties and prove the representation theorem in terms of particular order reversing involution on the co-domain poset. We prove that for every set of alternatives...

Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras

Leonardo Cabrer, Sergio Celani (2006)

Open Mathematics

In this work we give a duality for many classes of lattice ordered algebras, as Integral Commutative Distributive Residuated Lattices MTL-algebras, IMTL-algebras and MV-algebras (see page 604). These dualities are obtained by restricting the duality given by the second author for DLFI-algebras by means of Priestley spaces with ternary relations (see [2]). We translate the equations that define some known subvarieties of DLFI-algebras to relational conditions in the associated DLFI-space.

Quantum logics and bivariable functions

Eva Drobná, Oľga Nánásiová, Ľubica Valášková (2010)

Kybernetika

New approach to characterization of orthomodular lattices by means of special types of bivariable functions G is suggested. Under special marginal conditions a bivariable function G can operate as, for example, infimum measure, supremum measure or symmetric difference measure for two elements of an orthomodular lattice.

Restricted ideals and the groupability property. Tools for temporal reasoning

J. Martínez, P. Cordero, G. Gutiérrez, I. P. de Guzmán (2003)

Kybernetika

In the field of automatic proving, the study of the sets of prime implicants or implicates of a formula has proven to be very important. If we focus on non-classical logics and, in particular, on temporal logics, such study is useful even if it is restricted to the set of unitary implicants/implicates [P. Cordero, M. Enciso, and I. de Guzmán: Structure theorems for closed sets of implicates/implicants in temporal logic. (Lecture Notes in Artificial Intelligence 1695.) Springer–Verlag, Berlin 1999]....

Roughness of Filters in Lattice Implication Algebras

Y. B. Jun, Yang Xu (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

As a generalization of filters in lattice implication algebras, the notion of rough filters in lattice implication algebras is introduced, and some of their properties are considered.

Sobre funciones de negación en [0,1].

Francesc Esteva, Xavier Domingo (1980)

Stochastica

In [12] Trillas proved that (P(X),∩,U,-n) is a quasi-Boolean algebra if and only if its negation has an additive generator. In this paper such result is generalized to PJ(X) and the symmetry of J is analized.From the results of Esteva ([11]) weak negations on [0,1] are studied; it is proved that such functions are monotonic, non-increasing, left-continuous and symmetrical with respect to y=x. Their classification relative to C([0,1]) is also given and a canonical element of each class is found....

Some properties of Eulerian lattices

R. Subbarayan, A. Vethamanickam (2014)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we prove that Eulerian lattices satisfying some weaker conditions for lattices or some weaker conditions for 0-distributive lattices become Boolean.

Some remarks on distributive semilattices

Sergio A. Celani, Ismael Calomino (2013)

Commentationes Mathematicae Universitatis Carolinae

In this paper we shall give a survey of the most important characterizations of the notion of distributivity in semilattices with greatest element and we will present some new ones through annihilators and relative maximal filters. We shall also simplify the topological representation for distributive semilattices given in Celani S.A., Topological representation of distributive semilattices, Sci. Math. Japonicae online 8 (2003), 41–51, and show that the meet-relations are closed under composition....

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