This paper deals with the revision of partially ordered beliefs. It proposes a semantic representation of epistemic states by partial preorders on interpretations and a syntactic representation by partially ordered belief bases. Two revision operations, the revision stemming from the history of observations and the possibilistic revision, defined when the epistemic state is represented by a tot...

The elements of a finite nonempty partially ordered set are exposed at independent uniform times in [0,1] to a selector who, at any given time, can see the structure of the induced partial order on the exposed elements. The selector’s task is to choose online a maximal element. This generalizes the classical linear order secretary problem, for which it is known that the selector can succeed wit...

For example, thus far, I had the fortune to work intimately with nine (9) undergraduate students on research questions in the areas of computational algebra and algebraic geometry. I am directing two master’s students in their research for their theses at Sam Houston State University. All of these undergraduate students have enrolled in graduate programs around the country. Three have finished ...

A partial order on a set A induces a partition of each power An into “patterns” in a natural way. An operation on A is called a -pattern operation if its restriction to each pattern is a projection. We examine functional completeness of algebras with -pattern fundamental operations.

Let P be a partially ordered set and let Pp denote the set of all order-preserving mappings of P to P ordered by/ < g in Pp iif(p) < g(p) for all p £ P. We prove that if P and Q are finite, connected partially ordered sets and Pp = Q<¡ then Psg. Is a partially ordered set determined by its order-preserving mappings? L. M. Gluskin [4] has shown that the set of order-preserving mappings of a part...

The theory of simplicial sets and their realization is perhaps the basis to the combinatorial approach to homotopy theory. The construction of the geometric realization is very natural except for one thing: It begins with the postulation of the geometric realization of each of the “standard simplices”, to which no justification is given. It occurred to us that by “explaining” the nature of this...