Graphical notations for syllogisms: How alternative representations impact the accessibility of concepts

Abstract

Five notations for standard and multi-premise syllogisms are examined. Four are existing notations (verbal propositions, Euler diagrams, Venn diagrams and Englebretsen's Linear diagrams) and one a novel diagrammatic system – Category Pattern Diagrams (CPDs). CPDs integrate spatial location, linear ordering and properties of graphical objects in a comprehensive representational format to encode information about syllogisms, which provides a contrast to the use of degrees of spatial containment in the existing diagrammatic systems. The comparison of the five notations reveals how their underlying representational schemes can substantially impact the effectiveness of the encoding of the core concepts of the knowledge domain; in particular whether the core domain concepts are readily accessible as perceptual inferences and thus the notations are semantically transparent. The relative merits of CPDs provide some support for claims about the utility of the Representational Epistemic design principles that were used to create CPDs.