# 18.3 Earth, fire, water, air: Question

## Exercise: Earth, fire, water, air

The Greek philosopher Empedocles developed a theory of physical elements. He believed that everything was made up of four elements:

• Earth
• Fire
• Water
• Air

He furthermore believed that each of these was a mixture of one property from each of the following two sets of properties:

• Cold or hot
• Moist or dry

Each of the elements was made up as follows:

• Earth is cold and dry
• Fire is hot and dry
• Water is cold and moist
• Air is hot and moist

Draw a lattice depicting the type hierarchy that arises from these eight categories. It must have the properties cold, hot, moist, and dry at the top. At the bottom, it must have the four elements earth, fire, water, and air, and these must inherit from the four properties. Remember that multiple inheritance is possible. Also remember to include the two types Entity and Absurdity in the lattice.

Also, write a linear representation of the type hierarchy in the syntax of Prolog+CG.