Contemporary syllogistics: Comparative and quantitative syllogisms
Abstract
Traditionally, syllogisms are arguments with two premises and one conclusion
which are constructed by propositions of the form “All… are…” and “At least
one… is…” and their respective negated versions. Unfortunately, the practical use of
traditional syllogisms is quite restricted. On the one hand, the “All…” propositions are
too strict, since a single counterexample suffices for falsification. On the other hand,
the “At least one …” propositions are too weak, since a single example suffices for
verification. The present contribution studies algebraic interpretations of syllogisms
with comparative quantifiers (e.g., “Most… are…”) and quantitative quantifiers (e.g.,
“n/m… are…”, “all, except n… are…”). This modern version of syllogistics is intended
to be a more adequate framework for argumentation theory than traditional syllogistics.