Note on inter-expressibility of logical connectives in finitely-valued Godel-Dummett logics

摘要

Let G(m) be the m-valued Godel-Dummett fuzzy logic. If m >= 3 then neither conjunction nor implication is in G(m) expressible in terms of the remaining connectives. This fact remains true even if the propositional language is enriched by propositional constants for all truth values.