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.

Paula Teijeiro (Ph.D - University of Buenos Aires) is a CONICET postdoctoral fellow at IIF (SADAF-CONICET) and a member of the Buenos Aires Logic Group. Her research is focused on philosophical logic. Her main interests revolve around philosophy of logic, specially involving non-classical logics. In particular, she studies non-classical logics as they are used to deal with truth and vagueness-related paradoxes, both in formal theories and in natural language. Lately, her research focuses on theories in which some classically valid metainferences fail, such as substructural logics, and s-valuationism. She is a member of the BA logic group and an assistant professor at UBA, where she teaches Logic and Philosophy of science. She published papers in Thought, Logic and Logical Philosophy and Logic journal of the IGPL.
Eduardo Alejandro Barrio (Ph.D - University of Buenos Aires) is a full professor (tenure track) at University of Buenos Aires, a principal researcher at IIF (SADAF-CONICET) and a member of the Buenos Aires Logic Group (BA-LOGIC). He works in non-classical logics and philosophy of logic. He is mainly interested in substructural logics. His most important papers have high international impact, mainly published by Journal of Philosophical Logic, Review of Symbolic Logic, Studia Logica, Analysis, Synthese, Journal of Applied Non-Classical Logics and Logical Journal of IGPL. He has published three books: La Verdad Desestructurada (Buenos Aires, EUDEBA, 1998), Paradojas, Paradojas y más Paradojas (Londres, College PU, 2014) and La Lógica de la Verdad (Buenos Aires, EUDEBA, 2014). He has also been a guest editor in Logical Journal of IGPL (two times) and Journal of Philosophical Logic.