There are four qualifiers in term logic, organized according to two distinctions: particular/universal (some versus all) and affirmative/negative (permitting none and not all).
There are 256 combinations of these quantifiers in the form of a syllogism. One is 'AAA', or
(all x are y) and (all y are z) implies (all x are z).
Out of these 256, only 24 combinations are valid. Is there an effective strategy to generate these 24 valid forms, possibly from simpler rules relating to the quantifiers? (For instance:
all implies some...?)