An account of Aristotle's syllogistic (including a full square of opposition and allowing for empty nouns) as an integral part of first-order predicate logic is lacking. Some say it is not possible. It is not found in the tradition stemming from Łukasiewicz's attempt nor in less formal approaches such as Strawson's. The Łukasiewicz tradition leaves Aristotle's syllogistic as an autonomous axiomatized system. In this paper Aristotle's syllogistic is presented within first-order predicate logic with special restricted quantifiers. The theory is not motivated primarily by historical considerations but as an accurate account of categorical sentences along lines suggested by recent work on natural language quantifiers and themes from supposition theory. It provides logical forms which conform to grammatical ones and is intended as a rival to accounts of quantifiers in natural language that appeal to binary quantifiers, for example, Wiggins or to restricted quantifiers, for example, Neale.
"Reconciling Aristotle and Frege." Notre Dame J. Formal Logic 40 (3) 391 - 413, Summer 1999. https://doi.org/10.1305/ndjfl/1022615618