Universal logic as a science of patterns

Brian R. Gaines

pp. 145-189

in: Arnold Koslow, Arthur Buchsbaum (eds), The road to universal logic I, Basel, Birkhäuser, 2015

Abstract

This article addresses Béziau's (Sorites 12:5–32, 2001) vision that universal logic should be capable of helping other fields of knowledge to build the right logic for the right situation, and that for some disciplines mathematical abstract conceptualization is more appropriate than symbolic formalization. Hertz's (Math. Ann. 87(3–4):246–269, 1922) diagrams of logical inference patterns are formalized and extended to present the universal logic conceptual framework as a comprehensible science of patterns. This facilitates those in other disciplines to develop, visualize and apply logical representation and inference structures that emerge from their problématique. A family of protologics is developed by resemantifying the sign for deduction, →, with inference patterns common to many logics, and specifying possible constraints on its use to represent the structural connectives and defeasible reasoning. Proof-theoretic, truth-theoretic, intensional and extensional protosemantics are derived that supervene on the inference patterns. Examples are given of applications problem areas in a range of other disciplines, including the representation of states of affairs, individuals and relations.