# Intellectics Group: Technical Report 96-05

## Reasoning about Continuous Processes

### Christoph Herrmann and Michael Thielscher

Overcoming the disadvantages of equidistant discretization of
continuous
actions, we introduce an approach that separates time into slices of varying
length bordered by certain events. Such events are points in time at which the
equations describing the system's behavior---that is, the equations which
specify the ongoing *processes*---change. Between two events
the system's parameters stay continuous.
A high-level semantics for drawing logical
conclusions about dynamic systems with continuous processes is presented, and
we have developed an adequate calculus to automate this reasoning process.
In doing this, we have combined deduction and numerical calculus,
offering logical reasoning about precise, quantitative system information.
The scenario of multiple balls moving
in 1-dimensional space interacting with a pendulum serves as
demonstration example of our method.