A meaning based information theory - informalogical space: Basic concepts and convergence of information sequences

摘要

This paper presents an information theory that is based on meanings and relationships between information It first introduces the foundation of our approach, it binary relation contain between two pieces of information, based on inference between the two pieces of information Then, based on the contain relation, it introduces two basic operations union and intersection on a collection (i.e., set) of information. This paper lays the foundation of our approach by introducing the core concept, informalogical space. An informalogical space is a collection of information that satisfies certain conditions represented in terms of the contain relation, and the union and intersection operations. An informalogical space is similar to a topological space in a symbolic sense, but is different in nature This paper also introduces an information net in an informalogical space. An information net is a generalization of information sequence, just as a net is a generalization of sequence in general topology This paper builds a convergence theory for information nets that is similar in a symbolic sense to the Moore-Smith convergence theory in general topology. Then, this paper applies the results for information nets to information sequences.