Aristotle's Underlying Logic

Aristotelian Syntax from a Computational–Combinatorial Point of View

“…In presenting a minimal formal background for research into the Aristotelian sollogistics, it is dicult to avoid taking position in a, by now classical, dispute on the 'correct' way of formalising Aristotelian logic. George Boger ([1], [2] ) named the three main lines of interpretative trends regarding the Prior Analyics traditionalists, axiomaticists, and deductionists. ukasiewicz is the most prominent axiomatist, Corcoran and Smiley are, in Boger's terminology, deductionists.…”

“…'man', animal', 'living being', ...). For the sake of simplicity, we also use the symbols x, y, z, ...for elements of T. (2) There are four logical constants, A, E, Iand O, sometimes called Aristotelian quantors.…”

“…In standard mathematical terminology, a reduction relation is simply a strict antisymmetric relation, and this notion has absolutely nothing in common with the classical term 'reduction', being often used for the Aristotelian process of the deduction of derived rules. See Boger ([1], [2] ) for a thorough investigation of the terms used by Aristotle. Our terminology 'derivation of syllogisms' has the advantage that it goes well together with the concept of derived rules.…”

“…Unlike the aforementioned authors, however, we aim to position Aristotelian logic within the sphere of computational-combinatorical research methods. This is to provide a solid formal fundament for further computeraided research into this ancient system of formal logic 2 .…”

“…http://www.w3.org for detailled information. 2 It goes without saying that we will have to bridge abysses in trying to provide our methods and results in a form which make them accessible for those interested in the interpretation of classical Aristotelian logic as well as for those concerned with the properties of the formal system. 3 We plan to treat semantic matters in a subsequent paper.…”