Metainferences in Substructural Logics

This book provides a comprehensive overview of different logics from a metainferential standpoint. It starts with a metainferential presentation of Classical Logic, and then moves onto other systems where one or more structural metainferences fail. These logics maybe considered non-classical in a robust sense, since they allow to build theories which are non-transitive, non-reflexive, non-monotonic and non-contractive. In some other sense, though, they also preserve many desirable features of classical logics, and thus may have an advantage over other non-classical alternatives. The authors show how these logics can be characterized both model and proof-theoretically. Besides some standard inferential properties, emphasis is placed on metainferential theorems, some of them quite standard, such as Cut-elimination, and other more idiosyncratic, such as metainferential Soundness and Completeness. It ends with a philosophical chapter which intends to illustrate some of these logics' applications, mainly regarding non-classical treatments of paradoxes. Each chapter comes with exercises which help fix the central concepts, learn to use some of the formal tools, and problematize the philosophical issues at stake. This book is aimed to anyone interested in the question of reasoning, argumentation and theory-building in the presence of contradictions, paradoxes and other puzzles.