Since Robert Boyle’s corpuscularian philosophy, chemistry has been a mereological science. Displacing the metaphysics of `continuous substances’ and `qualities’ as the expression of “principles”, chemistry has been built on a `part-whole’ metaphysics. The grammar for the use of `part-whole’ concepts is mereology. Taking chemistry to be the science of the transformation of substances by the mani...

It is shown that the numbers ci of chains of length i in the proper part L\{0, 1} of a distributive lattice L of length ` + 2 satisfy the inequalities c0 < . . . < cb`/2c and cb3`/4c > . . . > c`. This proves 75 % of the inequalities implied by the Neggers unimodality conjecture.

We study the higher Bruhat orders B(n, k) of Manin & Schechtman [MaS] and-characterize them in terms of inversion sets,-identify them with the posets ZY(C n+1 ' r ,n+l) of uniform extensions of the alternating oriented matroids C n ' r for r := n—k (that is, with the extensions of a cyclic hyperplane arrangement by a new oriented pseudoplane),-show that B(n, k) is a lattice for k = 1 and for r ...

Methods of symbolic computation in the presence of imprecision and uncertainty of information are important to many areas of computational mathematics. They are fundamentally important to the Semantic Web and generally important to other areas such as Artificial Intelligence. When fully realized, the Semantic Web will enable wide spread sharing and integration of machine stored information and ...

the aim of this paper is to introduce and study set- valued homomorphism on lattices and t-rough lattice with respect to a sublattice. this paper deals with t-rough set approach on the lattice theory. the result of this study contributes to, t-rough fuzzy set and approximation theory and proved in several papers. keywords: approximation space; lattice; prime ideal; rough ideal; t-rough set; set...

Abstract A number of philosophers have argued in favour extended simples on the grounds that they are needed by fundamental physics. The arguments typically appeal to theories quantum gravity. To date, argument has ignored fact very existence spacetime is put under pressure We thus consider case for context different views spacetime. show based physics far more complex than been previously thou...