Propositional Logic is Too Weak a Representational Language
Propositional Logic (PL) is not a very expressive language because:
- Hard to identify "individuals." E.g., Mary, 3
- Can't directly talk about properties of individuals
or relations between individuals. E.g., tall(Bill)
- Generalizations, patterns, regularities can't easily
be represented. E.g., all triangles have 3 sides
Consider the problem of representing the following information:
- Every person is mortal.
- Confucius is a person.
- Confucius is mortal.
How can these sentences be represented so that we can infer the third
sentence from the first two? In PL we have to create propositional
symbols to stand for all or part of each sentence. For example, we
might do:
- P = "person"
- Q = "mortal"
- R = "Confucius"
so the above 3 sentences are represented as:
and though in this case the third sentence is entailed by the
first two, we needed an explicit symbol, R, to represent an individual,
Confucius, who is a member of the classes "person" and "mortal."
So, to represent other individuals we must introduce separate symbols
for each one, with means for representing the fact that all individuals
who are "people" are also "mortal." First-Order Logic (abbreviated
FOL or FOPC) is expressive enough to
concisely represent this kind of situation.