An extended syllogistic system with verbs and proper nouns, and its completeness proof
Noritaka, Kenichi, Shigenori · Systems and Computers in Japan · 1990
Abstract Syllogism (Aristotle's categorical syllogism) is a logic scheme which can describe derivation relations of propositions stating relations among quantified “terms” (corresponding to common nouns). In this system, relations of the terms are treated directly, while in predicate logic they are decomposed into relations among individual objects. Therefore, syllogism has several advantages in describing the meanings of a natural language in a formal framework of a logic system. However, the expressive ability of classical syllogism is poor in that it can treat only a proposition corresponding to a sentence whose predicate is “be” + noun (i.e., “is‐a” sentence) and cannot treat a sentence with a general verb (or “be” + adjective) in its predicate (we call it a verb sentence). Furthermore, terms in classical syllogism are only those corresponding to common nouns, and thus proper nouns, which cannot be quantified, are excluded.