On semi-Peano algebras

A semi-Peano algebra is an algebra for which each operation is injective, and the images of the operations are pairwise disjoint. The most straightforward non-trivial kind of finitely presented semi-Peano algebra are algebras with a single unary operation. There are two possible directions of generalization: algebras with a single operation of any arity, and algebras with several unary operations. The former can be solved easily by adapting results on equidecomposable groupoids from [2]. However, the second way is somewhat different. We will show that a finitely presented multi-unary semi-Peano algebra is the free product of cyclic semi-Peano algebras and that a unique relation defines such cyclic algebras. In addition, we will characterize each cyclic algebra up to isomorphism.Comment: 12 pages, 3 figure

Modern Interfaces for Knowledge Representation and Processing Systems Based on Markup Technologies

The usage of markup technologies to specify knowledge to be processed according to a specific field of application is a common technique. Representation techniques based on markup language paradigm to describe various types of knowledge including graph based models is considered and details on using Knowledge Representation and Processing (KRP) Systems in education are presented. XML, and VoiceXML were selected to implement smart interface for KRP systems