On the applicability of nonmonotonic logic to formal reasoning in continuous time

Abstract

The paper criticizes arguments recently advanced by Shoham, McDermott and Sandewall, which purport to demonstrate the relevance of nonmonotonic logic to the formalization of reasoning about the evolution of mechanical systems in continuous time. The first half of the paper examines the “Extended Prediction Problem” of Shoham and McDermott; reasons are given to support the claim that the “problem” is the product of a mistaken understanding of the formal basis of Newtonian mechanics, and has no real existence. An example is given showing how, contrary to Shoham and McDermott's arguments, it is possible to formalize reasoning about the evolution of physical systems in continuous time using only classical logic and differential calculus. The second half then reviews Sandewall's nonmonotonic logic for almost-continuous systems. Here it is argued that the proposed framework offers only very marginal advantages in compactness of notation, and generally tends to collapse back into classical logic. In summary, I conclude that there is as yet no good reason to believe that nonmonotonic logic will be a useful tool in this area.