Reasoning with limited resources: An LDS-based approach

Reasoning with limited computational resources (such as time or memory) is an important problem, in particular in knowledge-intensive embedded systems. Classical logic is usually considered inapropriate for this purpose as no guarantees regarding deadlines can be made. One of the more interesting approaches to address this problem is built around the concept of active logics. Although a step in the right direction, active logics still do not offer the ultimate solution. Our work is based on the assumption that Labelled Deductive Systems offer appropriate metamathematical methodology to study the problem. As a first step, we have reformulated a pair of systems, namely the step logic and the memory model proposed by Elgot-Drapkin, as Labelled Deductive Systems. This paper presents our motivation behind this project and presents in some detail the first system.