Nearness Rules and Scaled Proximity (Extended Version)

An artificial intelligence system that processes geo-thematic data would profit from a (semi-)formal or controlled natural language interface that incorporates concepts for nearness. Though there already exists logical-engineering approaches giving sufficient conditions for nearness relations, we show within a logical analysis that these suffer from some deficiencies. Non-engineering approaches to nearness such as the abstract mathematical approach based on proximity spaces do not deal with the implementation aspects but axiomatically formalize intuitions on nearness relations and provide insights on their nature. Combining the ideas of the engineering approach with the mathematical approach of proximity spaces, we define and analyze new nearness relations that provide a good compromise between implementation needs and the need for an appropriate approximation of the natural nearness concept.