Abstract

Building on Miller’s (1938) work, this paper employs reduced truth tables—which exclude empty terms and preserve traditional oppositional relations—to analyze logical equivalences among categorical propositions containing negated terms. It is demonstrated that: (1) every basic logical equivalence (e.g., “A belongs to every B” ↔ “Non-A belongs to no B”) generates a complementary version (“Non-A belongs to every non-B” ↔ “A belongs to no non-B”) through uniform term complementation. (2) This property of closure under complementation explains the internal consistency of Aristotle’s treatment of indefinite terms. The resulting system successfully preserves valid syllogistic modes within a broader and more unified semantic architecture.