Understanding the Axioms and Assumptions of Logical Mathematical Systems through Raster Images: Application to the Construction of a Likert Scale

Abstract

This article presents different artistic raster images as a resource for correcting misconceptions about different laws and assumptions that underlie the propositional systems of binary logic, Łukasiewicz’s trivalent logic, Peirce’s trivalent logic, Post’s n-valent logic, and Black and Zadeh’s infinite-valent logic. Recognizing similarities and differences in how images are constructed allows us to deepen, through comparison, the laws of bivalence, non-contradiction, and excluded middle, as well as understanding other multivalent logic assumptions from another perspective, such as their number of truth values. Consequently, the first goal of this article is to illustrate how the use of visualization can be a powerful tool for better understanding some logic systems. To demonstrate the utility of this objective, we illustrate how a deeper understanding of logic systems helps us appreciate the necessity of employing Likert scales based on the logic of Post or Zadeh, which is the second goal of the article.

Keywords

• fuzzy logic
• bivalent logic
• multivalent logic
• conceptual image
• laws of logic