This book offers an in-depth exploration of sequent calculi, highlighting their significance alongside more familiar proof systems. It covers a diverse array of non-classical logics, such as intuitionistic, relevance, linear, and modal logics. The author details various proof systems, emphasizing the development of cut theorems and decidability theorems. This comprehensive treatment aims to enhance understanding and appreciation of sequent calculi within the broader context of logic.
Focusing on the versatility of combinatory logic, this comprehensive reference explores its connections to philosophical, mathematical, and computational logic. It presents results from the past four decades alongside classical information, making the subject accessible. The author simplifies complex concepts while providing practical examples and applications, catering to both newcomers and those familiar with the field.
This book celebrates and expands on J. Michael Dunn’s influential work on informational interpretations of logic. Dunn introduced a semantics for first-degree entailments in his 1966 Ph.D. thesis, highlighting how sentences convey positive or negative information about topics. His interpretation of the logic R-mingle marked one of the first relational semantics for relevance logic, utilizing an incompatibility relation between information states to define negation. This theme of informational semantics extends to Dunn’s research on quantum logic, linear logic, and the theory of generalized Galois logics (or "gaggles"). His latest work explores informational interpretations of the ternary accessibility relation and the essence of information itself. The book opens with Dunn’s autobiography and a list of his publications, followed by a series of papers from respected logicians addressing various aspects of information-based logics. Topics include the applications of R-mingle in mathematical reasoning and its significance for other relevance logics, as well as interpretations of accessibility relations in non-classical logics. The collection also develops semantics for various logics, including modal and many-valued logics. This timely publication, reflecting our current "information age," offers new technical findings, intellectual history, and insightful expositions, appealing to a broad audience of scholars and researchers.