(joint work with Soma Dutta)

In one of the papers by Pelta et.al in Mathware and soft computing, the authors made a remark that Until now the construction of superficial many-valued logics, that is, logics with an arbitrary number (bigger than two) of truth values but always incorporating a binary consequence relation, has prevailed in investigations of logical many-valuedness. This remark seems to be a genuine observation although calling the entire tradition of many valued logics superficial is unwarranted. However, in 1986 one of the present authors made an attempt to address this issue and subsequently some other researchers continued work on this idea. Prior to this, fuzzy logic was already magnificently developed by Pavelka and others. Apparently it may seem that fuzzy logic deals with many-valuedness in the notion of consequence. In fact, there are evidences of such claims in the existing literature. The main objective of this paper is to show that this is not the case, that is fuzzy logics have never delved into lifting many valuedness to the meta-level. On the other hand the notion of graded consequence has taken up this issu