I'm getting toward this problem purely by natural language statements. Feel free to use convetional logic symbols in the answer.
Say we instantiate knowledge base with these predicates:
Universal
All human parents are either dads or moms
Men are not women
All dads are men
All moms are women
Existential
John is a man -> (add john to men as true and women as false)
Erica is a mom -> (add erica to moms, all moms are added to women and to human parents, also add erica to men as false)
Then we want to ask few questions:
Propositions
Is John a dad? -> (John in Dads) -> don't know, because john is a man, but it is not stated if he is a dad or evan a parent
Is John a man? -> (John in Men) -> true
Is John a woman? -> (John in Women) -> false
Is Erica a man? -> (Erica in Men) -> false
Is Erica a woman? -> (Erica in Women) -> true
Is Erica a human parent? -> (Erica in HumanParents) -> True
Problematic parts
a) I find these part problematic, say if predicate is created:
John is a man
John is a parent
Should we add John to dads at this state because we know he is a man. Or should there be a separate predicative clause for it?
b) What if predicate is created in this manner:
John is a parent
And knowledge base is asked in a proposition:
Is John either a man or a woman? -> True?
Or should there be separate predicative clauses to handle this kind of query?
c) Finally, what is the right result in case symbols are not known:
Is Erica a daughter -> (Erica in Daugthers) -> don't know, there are no daughters available
Is Steve a man -> (Steve in Men) -> don't know, Steve is not stated before
I'd appreciate any input given.
Currently, your axioms describe the following situation: you implicitly seem to have a population/universe of humans, i.e. variables range over humans.
Within humans, there are two disjoint sets, men and women. However, these do not need to cover all of humans -- there is no axiom stating that everyone is either a man or a woman. So there could be humans which are neither men or women.
Within men, there is a subset of people called "dads". It does not follow that all men are also dads. Similarly, within women, there is a subset of people called "moms"; again, these are not necessarily the whole set of women.
Then, there is a set of parents, which is a subset of dads $\cup$ moms; however, since there is no axiom stating that a dad is a parent, or that a mom is a parent, you cannot rule out that there are dads or moms which are not parents.
Furthermore, you have John somewhere in the category "men"; this means he could be a dad and even a parent, but we don't know. We do know that he is not a woman (and by extension not a mom). Erica is a mom, which in particular means she is a woman and therefore not a man (and not a dad); however, without additional axioms, you cannot prove that she is a parent.
Thus, with your sentences, the following necessarily hold:
The following might be true, but cannot be derived from the axioms:
The following are definitely false:
The following are meaningless, because they use symbols ("daughter", "Steve") you have not defined. Alternatively you could take the point of view that they are simply symbols for which you have no axioms, in which case both of them fall into "might be true" category; but note that if you take that point of view a sentence like "If Erica is a daughter then Erica is a daughter" would fall into the first category.