THE PRINCIPLES OF NON-CONTRADICTION AND EXCLUDED-MIDDLEIN FUZZY LOGIC, REVISITED

摘要

This paper just tries to revisit the Aristotelian principles of Non-Contradiction and Excluded-Middle with fuzzy sets. In the first place, it is proven that there are many standard theories that verify such principles if posed in the typical ways μ.μ'= [μ_0 and μ + μ' respectively. In the second place, a different form of posing the principles is considered, and it is proven that they are theorems in the framework of the very general structure of a Basic Fuzzy Algebra, of which the standard algebras of fuzzy sets are a functionally expressible particular case.