
TL;DR
This paper introduces fuzzy Aristotelian Diagrams within a mathematical universe, extending classical diagrams to fuzzy logic, and discusses their properties and the underlying logical framework.
Contribution
It presents a novel mathematical formulation of fuzzy Aristotelian Diagrams and characterizes the universe hosting these fuzzy logical objects.
Findings
Fuzzy Aristotelian Diagrams are formally defined within a mathematical universe.
The paper extends classical diagrams to accommodate fuzzy logic.
Characteristics of the mathematical universe supporting fuzzy diagrams are outlined.
Abstract
After a concise introduction to the square of opposition, in particular, and, Aristotelian Diagrams, in general, I describe how one can create a mathematical universe to host these objects. Since these objects assume that the underlying logic is the bivalent logic, I have used these objects as a starting point to introduce fuzzy Aristotelian Diagrams and describe a mathematical formulation of them. In addition, I outline the characteristrics of a mathematical universe that hosts them.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rough Sets and Fuzzy Logic · Logic, Reasoning, and Knowledge
