##
John Pfaltz, Professor

**
``Discrete systems are dynamic, but how do we describe their change?
The calculus doesn't help us here''.
**

**
Contihnuity is seldom mentioned when discussing discrete systems.
This is a mistake!
**

The notion of functional transformations that preserve the structure
of the domain is fundamental to all science.

If a function is "continuout", similar inputs should be mapped
to similar outputs; why do we not ask if procedures are "continuous?''

**Office: 211 Reid Hall**

**Office Phone: (804) 982-2222**

**E-mail: pfaltz@virginia.edu**

**US Mail:**

**Department of
Computer Science**

**Thornton Hall**

**University of Virginia,**

**Charlottesville, VA 22903**

**USA**
## **Current Research:**

Our current emphasis is on *closure systems* and their
applications to cognitive science
These closure systems provide a formal mechanism for studying the nature of
discrete systems which are the ``stuff'' of cognitive science and many
other empirical scieces.
Moreover, they permit the definition of *continuous transformations*
which are functions on discrete systems.
When the discrete systems are concept spaces, discrete continuity models a
basic form of learning.
The ADAMS database language represents earlier research,
but it is no longer an active program.
The implemented system is rather unique, and and its suffix based notation
has been carried over into our theoretial research.
Even though we are not expanding the ADAMS program, it has aspects that are
well worth examining.
We will provide source code to those interested in implementing this object
oriented database system.