Taking Degrees of Truth Seriously

摘要

This is a contribution to the discussion on the role of truth degrees in many-valued logics from the perspective of abstract algebraic logic. It starts with some thoughtson the so-called Suszko's Thesis (that every logic is two-valued) and on the conceptionof semantics that underlies it, which includes the truth-preserving notion of consequence.The alternative usage of truth values in order to define logics that preserve degrees oftruth is presented and discussed. Some recent works studying these in the particular casesof Lukasiewicz's many-valued logics and of logics associated with varieties of residuatedlattices are also presented. Finally the extension of this paradigm to other, more generalsituations is discussed, highlighting the need for philosophical or applied motivations inthe selection of the truth degrees, due both to the interpretation of the idea of truth degreeand to some mathematical difficulties.