Modelling the Qualitative World

Qualitative physics seeks to understand physical processes by building models of them.

A model may consist of the following entities:

Variables

-- make take on values as in a traditional physics model but with a restricted set of values, e.g. temperature as .

Quantity Spaces

-- a small set of discreet values for a variable.

Rate of Change

-- Variables take on different values at different times. A real valued rate of change can be modelled qualitatively with a quantity space, e.g. .

Expressions

-- Combination of variables.

Equations

-- Assignment of expression to variables.

States

-- Sets of variables who's values change over time.

Note that qualitative algebra is different:

Say we describe the volume of glass as

Then when we add two qualitative values together we get: