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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Logic · Rough Sets and Fuzzy Logic · Logic, Reasoning, and Knowledge