Euler Diagrams for Defeasible Reasoning

Abstract

We investigate Euler diagrammatic systems for defeasible reasoning by extending the usual systems for Euler and Venn diagrams corresponding to standard classical logic. To achieve this, we use the generalized quantifier “most” to formalize defeasible reasoning, as proposed by Schlechta (1995), where defeasible knowledge is represented as “Most A are B” and axioms for “most” are defined. We introduce an Euler diagrammatic system for defeasible reasoning by introducing circle mA that represents “most A” for each circle A. We show that our Euler diagrammatic system is a diagrammatic representation of the symbolic system of the generalized quantifier “most”. Furthermore, we investigate skeptical and credulous strategies in defeasible reasoning with our Euler diagrams.