In connection with the emerging theory of Garside categories, we develop the notions of a left-Garside category and of a locally left-Garside monoid. In this framework, the connection between the self-distributivity law LD and braids amounts to the result that a certain category associated with LD is a left-Garside category, which projects onto the standard Garside category of braids. This appr...

We present a computational treatment of the semantics of plural Noun Phrases which extends an earlier approach presented by Scha [7] to be able to deal with multiple-level plurals ("the boys and the girls", "the juries and the committees", etc.) 1 We argue that the arbitrary depth to which such plural structures can be nested creates a correspondingly arbitrary ambiguity in the possibilities fo...

Abstract A classical theorem of Balcar, Pelant, and Simon says that there is a base matrix height ${\mathfrak h}$ , where the distributivity number ${\cal P} (\omega ) / {\mathrm {fin}}$ . We show if continuum c}$ regular, then are matrices any regular uncountable $\leq {\mathfrak in Cohen random models. This answers questions Fischer, Koelbing, Wohofsky.

A function f is AND bi-decomposable if it can be written as f (X1;X2) = h1(X1)h2(X2). In this case, a sum-ofproducts expression (SOP) for f is obtained from minimum SOPs (MSOP) for h1 and h2 by applying the law of distributivity. If the result is an MSOP, then the complexity of minimization is reduced. However, the application of the law of distributivity to MSOPs for h1 and h2 does not always ...

A. Huhn proved that the dimension of Euclidean spaces can be characterized through algebraic properties of the lattices of convex sets. In fact, the lattice of convex sets of IEn is n+1-distributive but not n-distributive. In this paper his result is generalized for a class of algebraic lattices generated by their completely join-irreducible elements. The lattice theoretic form of Carathédory's...