Subsection 7.5.3 Taming Vagueness in Describing the Everyday World
Consider the question of height:
[1] Professional basketball players are tall.
[2] Elephants are very tall.
[3] Giraffes are super tall.
Sometimes we make comparative statements:
Indian food is spicier than Irish food.
How shall we represent claims such as these in the logical language that we’ve defined? The answer is that it depends on how we want to reason with them.
One standard approach is to define a numeric scale (say 1 to 10). Then we can make numeric claims. We can specify cutoffs that define adjectives like tall.
If we want to be more sophisticated, we can make such cutoffs relative to a reference set.
For example, it’s possible to be a tall person at a height that would be in midget territory for a giraffe.
There are other digitizing issues that don’t so naturally correspond to numeric scales.
Suppose that I have an apple in the refrigerator. I take it out and eat one bit and put it back, I probably still have an apple in the fridge. What if I eat half the apple and put the rest back. Do I still have an apple in the fridge? What if I eat all but one bite?
A lot has been written about issues such as these. We’ll have to skip most of them for now. The key for us will be to stay focused on the reasoning that we want to do. Then we must make representation decisions that let us do that reasoning. We should never imagine that we’ve captured everything anyone might want to say.