On the extension of classical propositional logic by means of a triangular norm

In this article, we introduce a generalized extension principle by substituting a more general triangular norm T for the min intersection operator in Zadeh's extension principle. We also introduce a family of propositional logics, sup‐ T extension logics, obtained by the extension of classical‐logical functions. A few general properties of these sup‐ T extension logics are derived. It is also shown that classical binary logic and the Kleene ternary logic are special cases of these logics for any choice of T , obtained by a convenient restriction of the truth domain. the very practical decomposability property of classical logic is furthermore shown to hold for the sup‐min extension logic, albeit in a somewhat more limited form.