What is the fundamental insight behind truth-functionality? When is a logicinterpretable by way of a truth-functional semantics? To address such questions in asatisfactory way, a formal definition of truth-functionality from the point of view of abstractlogics is clearly called for. As a matter of fact, such a definition has been available at leastsince the 70s, though to this day it still remains not very widely well-known. A clear distinction can be drawn between logics characterizable through: (1) genuinelyfinite-valued truth-tabular semantics; (2) no finite-valued but only an infinite-valued truth-tabular semantics; (3) no truth-tabular semantics at all. Any of those logics, however, canin principle be characterized through non-truth-functional valuation semantics, at least assoon as their associated consequence relations respect the usual tarskian postulates. So,paradoxical as that might seem at first, it turns out that truth-functional logics may beadequately characterized by non-truth-functional semantics. Now, what feature of a givenlogic would guarantee it to dwell in class (1) or in class (2), irrespective of its circumstantialsemantic characterization? The present contribution will recall and examine the basic definitions, presuppositionsand results concerning truth-functionality of logics, and exhibit examples of logics indige-nous to each of the aforementioned classes. Some problems pertaining to those definitionsand to some of their conceivable generalizations will also be touched upon.
展开▼
