The Logic of Persistence

Abstract

A recent paper [Hanks19851 examines temporal reasoning as an example of default reasoning. They conclude that all current systems of default reasoning, including non-monotonic logic, default logic, and circumscription, are inadequate for reasoning about persistence. I present a way of representing persistence in a framework based on a generalization of circumscription, which captures Hanks and McDermott’s procedural representation. 1. Persistence The frame problem is that of representing a dynamic world so that one can formally infer the facts whose truth values are not changed by a given action. A temporal world model allows one to assert that various actions occur at various times, and to be silent about other times. When one reasons with such a model, the frame problem is generalized to the persistence problem: given that no relevant action, or perhaps no action at all, occurred over a stretch of time, one may need to infer that certain facts do not change their truth values over that time. [n other words, one needs to represent the “inertia ” of the world, the moment to moment persistence of many of its properties. Examples of persistence abound in everyday reasoning. Sitting in my office, I can infer that my car is in the parking lot, because that is where I left it this morning. IHanks examines the following example, here simplified. Assume a simple linear, discrete model of time, containing instants 1, 2, 3, etc. At time 1 John is alive, and a gun aimed at John is loaded. At time 3 the gun is fired. We know that if the gun is loaded when it is fired, John will die at the next moment of time. We would like to conclude that John is not alive at time 4. In order to do so, we must make the persistence inference that the gun stays loaded from times 1 to 3. (See figure