Simplified forms of computerized reasoning with distance semantics

The semantics of formalisms for representing dynamically evolving and possibly contradictory information is often determined by distance-based considerations. This implies that the reasoning process in such contexts, and the corresponding entailment relations, are induced, in one way or another, from an underlying metric space, in which distances are associated with measurements of plausibility. In this paper we show that in many cases such distance-based entailments can be computerized in a general and modular way. For this, we consider two different approaches for reasoning with distance semantics, one is based on set computations and the other one is defined by rule-based systems. These methods are then applied to some common cases of distance semantics, and the outcome is a specification of some simple and natural algorithms for reasoning in those frameworks. It is shown that what is obtained has some strong ties to well-known SAT-related problems.