In this paper, we define a property, trimness, for lattices. Trimness is a not-necessarily-graded generalization of distributivity; in particular, if a lattice is trim and graded, it is distributive. Trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity. The order complex of a trim lattice is contractible or homotopic to a sph...

In Yaeyaman, a critically endangered Japonic language of the Southern Ryukyus, there is a distinction made between singular and plural wh-questions, with plurality indicated by reduplication of the indeterminate (wh) pronoun. I argue that reduplication of the indeterminate is triggered by a morpheme RED that requires the presence of non-atoms in the set of Hamblin alternatives denoted by its si...

ABSTRACT. Inspired by the article of P. Grzegorzewski [The inclusion-exclusion principle for IF-events, Inform. Sci. 181 (2011), 536–546], who has worked two generalizations of the inclusion-exclusion principle for IF-events, a generalization of the inclusion-exclusion principle for mappings with values in semigroups is presented here. The main idea is in replacing the distributivity and idempo...

Examples of games between two partners with mixed strategies, calculated by the use of the probability amplitude as some vector in Hilbert space are given. The games are macroscopic ,no microscopic quantum agent is supposed. The reason for the use of the quantum formalism is in breaking of the distributivity property for the lattice of yes-no questions arising due to the special rules of games....

The main goal of this paper is to study the finite groups whose lattices of fuzzy subgroups are distributive. We obtain a characterization of these groups which is similar to a wellknown result of group theory. 2008 Elsevier Inc. All rights reserved.