Assessing Arguments with Schemes and Fallacies

Abstract

We present a logical framework allowing us to express assessment of facts (is it proven?) and arguments (is it sound?) together with a proof system to answer these questions. Our motivation is to clarify the notion of validity in the context of logic-based arguments along different aspects (such as the formulas used and the inference scheme). Originality lies in the possibility for the user to design their own argument schemes. We show that classical inference obtains when arguments are based on classical schemes (e.g. Hilbert axioms). We go beyond classical logic by distinguishing “proven” formulas from “uncontroversial” ones (whose negation is not proven). Hence a formal definition of a fallacious argument: it uses controversial formulas or schemes recognized as illicit. We express some rational arguments and fallacies in the form of schemes.