Neighborhood Systems and Approximation in Relational Databases and Knowledge Bases

In solving mathematical equations, it is often sufficient to find approximate solutions; in answering database queries, very often the situation is similar. To formulate the notion of approximation, the neighborhood system or topology is introduced into the relational model called topological data model. Moreover, when a knowledge base is derived from a database, a neighborhood system can also be introduced. The notion of topology in database and knowledge base supports the approximate retrieval and reasoning in the similar fashion the topology supports the approximate solutions in numerical analysis and functional analysis. The approximate reasoning here is different from the usual approximate reasoning that uses certainty factors. This paper is a step toward a formalization of what Dr. Hao Wang called "approximate proof" in his celebrated paper "Toward mechanical mathematics" and his subsequent papers for which he received, among other honors, the first Milestone Award in automated theorem-proving.