CICERO’S INFERENCE FROM A NON-AXIOMATIC SYSTEM

Abstract

Cicero posed a controversial claim. He proposed that the Stoics admitted an inference hard to accept. That inference is also incorrect in propositional calculus. It consists of two premises and a conclusion. The first premise is the negation of a conjunction. The second premise is the negation of one of the conjuncts of that conjunction. The conclusion provides that those premises allow deriving the truth of the other conjunct. My purpose here is not to analyze whetherthe inference can be valid in the general framework of Stoic logic. My intention is not to argue in favor of or against the idea that Cicero made a mistake either. The aim of the paper is only to show that a non-axiomatic logic can make inferences akin to that described by Cicero, and that, hence, an Artificial Intelligence system based on that logic can also do that. Two components of the logic are essential here: its inheritance copula and its concept of extensional difference.