A partiallyordered multiset or pomset is a generalizationof a string in which the total order has been relaxed to a partial order. Strings are often used as a model for sequential computation; pomsets are a natural model for parallel and distributed computation. By viewing pomsets as a generalization of strings, the question is raised whether concepts from language theory can be generalized to ...

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...

5 Goguen’s category of V-sets whose objects are functions with values in a pre-ordered set and morphisms are suitable maps is shown to be a topological construct if and only if the pre-ordered set is a complete lattice; in particular the category Set(L) of L-sets, 7 also considered by Goguen, is topological over Set. The special case when the considered pre-ordered set is L with the “mapping to...

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 ...