Expressivity and Control in Limited Reasoning

Real agents (natural or artificial) are limited in their reasoning capabilities. In this paper, we present a general framework for modeling limited reasoning based on approximate reasoning and discuss its properties. We start from Cadoli and Schaerf's approximate entailment. We first extend their system to deal with the full language of propositional logic. A tableau inference system is proposed for the extended system together with a sub-classical semantics; it is shown that this new approximate reasoning system is sound and complete with respect to this semantics. We show how this system can be incrementally used to move from one approximation to the next until the reasoning limitation is reached. We note that although the extension is more expressive than the original system, it offers less control over the approximation process. We then suggest how we can recover control while keeping the increased expressivity.