Consider the following argument:
- P1: A is a father.
- Therefore: A is a parent.
The above inference is analytic and valid: it is impossible that someone is a father without also being a parent. However, formalizing the above and similar inference as a valid argument seems beyond the power of either proportional or predicate logic.
For example, in predicate logic, we would get something like:
- P1: Fa
- Therefore: Pa
Which is not valid.
My question is, if proportional and predicate logic lack the power to express analytic inferences like the above, are there logics that can, and if so, which logic and how?