Metainferential Logics

This book is the first to present a comprehensive investigation of the technical features of the metainferential logics developed in the last years, with their most relevant results and applications. It provides some new paths to define and investigate metainferential logics and offers a thorough study of the semantics and the proof-theories of this new and exciting variety of families of logics. This volume examines the hierarchies of metainferential logics and gives a general and systematic theory of them, and of the truth theories based on these logics. This book puts forward the prospects for truth-theories based on the metainferential logics of the TS/ST hierarchy and argues for its promise noting that each of these logics can be safely expanded with a transparent truth predicate. It also goes onto to explore new developments in three fields related to logics – namely metainferential logics built by means of the Weak Kleene schema and combining them with logics defined through the Strong Kleene schema, proof-theoretic presentations, and those with a with a global or an absolutely global validity standard, instead of a local one. This book is of interest to scholars in formal logic.

This volume investigates what is beyond the Principle of Non-Contradiction. It features 14 papers on the foundations of reasoning, including logical systems and philosophical considerations. Coverage brings together a cluster of issues centered upon the variety of meanings of consistency, contradiction, and related notions. Most of the papers, but not all, are developed around the subtle distinctions between consistency and non-contradiction, as well as among contradiction, inconsistency, and triviality, and concern one of the above mentioned threads of the broadly understood non-contradiction principle and the related principle of explosion. Some others take a perspective that is not too far away from such themes, but with the freedom to tread new paths. Readers should understand the title of this book in a broad way,because it is not so obvious to deal with notions like contradictions, consistency, inconsistency, and triviality. The papers collected here present groundbreaking ideas related to consistency and inconsistency.

Reasons for Logic, Logic for Reasons presents a philosophical conception of logic—“logical expressivism”—according to which the role of logic is to make explicit reason relations, which are often neither monotonic nor transitive. This conception of logic reveals new and enlightening perspectives on inferential roles, sequent calculi, representation, truthmakers, and many extant logical theories. The book shows how we can understand different metavocabularies as making explicit the same reason relations, namely normative-pragmatic, alethic-representational, logical, and “implication-space” metavocabularies. This includes a philosophical account of the pragmatic role of reason relations, treatments of nonmonotonic and nontransitive consequence relations in sequent calculi, a correspondence between these sequent calculi and variants of truthmaker theory, and the introduction of a novel kind of formal semantics that interprets sentences by assigning inferential roles to them. The book thus offers logical expressivists and semantic inferentialists new ways to understand logic, content, inferential roles, representation, and reason relations. This book will appeal to researchers and graduate students who are interested in the philosophy of logic, in reasons and reasoning, in theories of meaning and content, or in nonmonotonic and nontransitive logics.

This book presents the state of the art in the fields of formal logic pioneered by Graham Priest. It includes advanced technical work on the model and proof theories of paraconsistent logic, in contributions from top scholars in the field. Graham Priest’s research has had a considerable influence on the field of philosophical logic, especially with respect to the themes of dialetheism—the thesis that there exist true but inconsistent sentences—and paraconsistency—an account of deduction in which contradictory premises do not entail the truth of arbitrary sentences. Priest’s work has regularly challenged researchers to reappraise many assumptions about rationality, ontology, and truth. This book collects original research by some of the most esteemed scholars working in philosophical logic, whose contributions explore and appraise Priest’s work on logical approaches to problems in philosophy, linguistics, computation, and mathematics. They provide fresh analyses, critiques, and applications of Priest’s work and attest to its continued relevance and topicality. The book also includes Priest’s responses to the contributors, providing a further layer to the development of these themes .

This LNCS book is part of the FOLLI book series and constitutes the proceedings of the 8th International Workshop on Logic, Rationality, and Interaction, LORI 2021, held in Xi`an, China, in October 2021. The 15 full papers presented together with 7 short papers in this book were carefully reviewed and selected from 40 submissions. The workshop covers a wide range on the following topics such as doxastic and epistemic logics, deontic logic, intuitionistic and subsstructural logics, voting theory, and (a new theme emphasized this year) causal inference.

This wide-ranging collection of essays explores the nature of logic and the key issues and debates in the metaphysics of logic.

Originally published in 1967. An introduction to the literature of nonstandard logic, in particular to those nonstandard logics known as many-valued logics. Part I expounds and discusses implicational calculi, modal logics and many-valued logics and their associated calculi. Part II considers the detailed development of various many-valued calculi, and some of the important metathereoms which have been proved for them. Applications of the calculi to problems in the philosophy are also surveyed. This work combines criticism with exposition to form a comprehensive but concise survey of the field.