Abstract

Prior to investigating the degree of maximality of a propositional logic, as is the notion introduced by Ryszard Wojcicki [8], it is important to determine all structural consequence stronger than the logic considered. This characterization of all structural strengthenings was performed while establishing the degree of maximality for Lukasiewicz and Lukasiewicz-like logics [8], [4], [9], [5]. In these papers the authors used matrix consequences together with certain results concerning this notion and a representation theorem for Lukasiewicz algebras as given by R. S. Grigolia [2].