Universal Logic as a Science of Patterns

Abstract. This article addresses Béziau’s [11] 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 concep-tualization is more appropriate than symbolic formalization. Hertz’s [67] dia-grams 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 proto-semantics 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