# Representing Continuous Change in the Event Calculus

# Murray Shanahan

## Abstract

The Event Calculus of Kowalski and Sergot only deals with discrete change.
This paper introduces a simplified version of the Event Calculus and
extends it to deal with continuous change, as in the height of a falling
object or the level of liquid in a filling vessel. The idea of
autotermination is introduced. A period of continuous change
autoterminates if it brings about the event which terminates it. For
example, when the increasing level of water in a sink reaches the overflow,
it ceases to increase. The formulation is applied to a simple example with
liquid filling a sink, and to a more complicated one with many tanks
discharging liquid into another tank.