Editorial Introduction: Substructural Logics and Metainferences

The concept of substructural logic was originally introduced in relation to limitations Gentzen’s structural rules Contraction, Weakening and Exchange. Recent years have witnessed the development logics also challenging Tarskian properties Reflexivity Transitivity logical consequence. In this introduction we explain recent two aspects which it leads a reassessment bounds classical logic. On one hand, standard ways defining notion consequence naturally induce when admitting more than truth values; on other these give rise hierarchies metainferences that can be used approximate at different levels.