Truth Diagrams Versus Extant Notations for Propositional Logic

Abstract

Truth diagrams (TDs) are introduced as a novel graphical representation for propositional logic (PL). To demonstrate their epistemic efficacy a set of 28 concepts are proposed that any comprehensive representation for PL should encompass. TDs address all the criteria whereas seven other existing representations for PL only provide partial coverage. These existing representations are: the linear formula notation, truth tables, a PL specific interpretation of Venn Diagrams, Frege's conceptual notation, diagrams from Wittgenstein's Tractatus, Pierce's alpha graphs and Gardner's shuttle diagrams. The comparison of the representations succeeds in distinguishing ideas that are fundamental to PL from features of common PL representations that are somewhat arbitrary.

Endowing Machines with the Expert Human Ability to Select Representations: Why and How

“…For example, for propositional calculus, diagrammatic representations are an alternative to the traditional formulae and truth table representations, which are commonly used for teaching. A review of Frege, Wittegnstein, Pierce and Gardner's representations by Cheng (2020) shows how their different formats substantially impact the accessibility of information: not just the content of propositional relations but also the form of inference rules and the strategic information needed to manage proof making. Cheng (2020) designed a novel diagrammatic representation for propositional calculus that makes directly accessible these multiple levels of information that are not easily available in the sentential and other representations (Figure 1.2a).…”

The puzzle of ideography

“…The idea of deploying semantic functions in the design of a graphic code is not purely theoretical. My own efforts at designing graphical notations for conceptually challenging information intensive topicsalbeit specialistshow that when such functions are satisfied, users find the new notations cognitively superior to conventional representations (e.g., Cheng, 2002Cheng, , 2011Cheng, , 2012Cheng, , 2020.…”