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

This paper presents an information theory that is based on meanings and relationships of information. This paper first introduces the very basic concept in our approach, a binary relation contain between two pieces of information, which is based on inference between the two pieces of information. Then, based on the contain relation, this paper introduces two basic operations union and intersection on a collection (i.e., set) of information. This paper lays the basis 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 symbolic sense, but is different in nature. This paper also introduces information net in an informalogical space. Information net is a generalization of information sequence, just like that net is a generalization of sequence in general topology. This paper will build a convergence theory of information net that is similar to the Moore-Smith convergence in general topology in symbolic sense. Then, this paper applies the results on information nets to information sequences.