A logic for best explanations. Issue 2 (3rd April 2019)

• Record Type: Journal Article
• Authors: Millson, Jared; Straßer, Christian
• Is Part Of: Journal of applied non-classical logics. Volume 29:Issue 2(2019)
• Page Start: 184
• Page End: 231
• Publication Date: 2019-04-03
• Subjects: Abduction -- inference to the best explanation -- defeasible reasoning -- sequent calculus; Nonclassical mathematical logic -- Periodicals; Wiskundige logica; Logic; Periodicals; 511.3105
• DOI: 10.1080/11663081.2019.1591108
• Languages: English
• ISSNs: 1166-3081

Abstract

ABSTRACT: Efforts to formalize qualitative accounts of inference to the best explanation (IBE) confront two obstacles: the imprecise nature of such accounts and the unusual logical properties that explanations exhibit, such as contradiction-intolerance and irreflexivity. This paper aims to surmount these challenges by utilising a new, more precise theory that treats explanations as expressions that codify defeasible inferences. To formalise this account, we provide a sequent calculus in which IBE serves as an elimination rule for a connective that exhibits many of the properties associated with the behaviour of the English expression 'That…best explains why…'. We first construct a calculus that encodes these properties at the level of the turnstile, i.e. as a metalinguistic expression for classes of defeasible consequence relations. We then show how this calculus can be conservatively extended over a language that contains a best-explains-why operator.