Pseudo-open functions are monotonic decreasing for ordinal and cardinal invariants

AbstractA new property of pseudo-open functions is presented in this paper. Pseudo-open functions are monotonic decreasing with respect to ordinal and cardinal invariants defined by compact and sequential closures. A weak form of continuity, called k-continuous, is defined, characterized and used in the proof of the monotonicity properties of pseudo-open mappings. The relationships between the classes of k-continuous and sequentially continuous mappings in the category of all topological spaces and the continuous mappings in the subcategories of k-spaces and sequential spaces are presented

Evaluating Knowledge Representation and Reasoning Capabilites of Ontology Specification Languages

The interchange of ontologies across the World Wide Web (WWW) and the cooperation among heterogeneous agents placed on it is the main reason for the development of a new set of ontology specification languages, based on new web standards such as XML or RDF. These languages (SHOE, XOL, RDF, OIL, etc) aim to represent the knowledge contained in an ontology in a simple and human-readable way, as well as allow for the interchange of ontologies across the web. In this paper, we establish a common framework to compare the expressiveness of "traditional" ontology languages (Ontolingua, OKBC, OCML, FLogic, LOOM) and "web-based" ontology languages. As a result of this study, we conclude that different needs in KR and reasoning may exist in the building of an ontology-based application, and these needs must be evaluated in order to choose the most suitable ontology language(s)