Aristotelian Syntax from a Computational-Combinatorial Point of View

This paper translates Aristotle’s syllogistic logic of the Analytica priora into the sphere of computational-combinatorical research methods. The task is accomplished by formalising Aristotle’s logical system in terms of rule-based reduction relations on a suitable basic set, which allow us to apply standard concepts of the theory of such structures (Newman lemma) to the ancient logical system. In this way we are able to reproduce Aristotle’s method of reducing syllogisms within a precisely defined formal environment, and we can analyse the structure of the set of syllogistic rules by means of a computer program. Thus we show that Aristotle’s syllogistic logic is a formal system of its own which can be modelled independently of predicate logic and set theory. Our research is very much in the spirit of Smiley’s and Corcoran’s modelling of Aristotelian logic as a deductional system, and we aim at staying close to Aristotle’s own term–logical concepts.