Time is fundamental in representing and reasoning about changing domains. A proper temporal representation requires characterizing two notions: (1) time itself, and (2) temporal incidence, i.e. the domain-independent properties for the truth-value of uents and events throughout time. There are some problematic issues such as the expression of instantaneous events and instantaneous holding of ue...

We determine the elementary divisors, and hence the rank over an arbitrary field, of the incidence matrix of the classical unital.

Given an algebra A we associate an incidence algebra A(Σ) and compare their Hochschild cohomology groups.

The investigation of symmetric designs is of central interest in design theory. Another class of important incidence structures are projective and affine geometries. A projective geometry gives rise to two symmetric designs, namely the point-hyperplane designs and their complements. It is a remarkable property of these classical symmetric designs that we will investigate in this paper. For the ...

Let X be any partially ordered set, R any commutative ring, and T = I * (X,R) the weak incidence algebra of X over R. Let Z be a finite nonempty subset of X, L(Z) = {x ∈ X : x z for some z ∈ Z}, and M = Te Z. Various chain conditions on M are investigated. The results so proved are used to construct some classes of right perfect rings that are not left perfect.