Perspectives On Universal Logic

Perspectives on Universal Logic

The Road to Universal Logic

This second volume of a collection of papers offers new perspectives and challenges in the study of logic. It is presented in honor of the fiftieth birthday of Jean-Yves Béziau. The papers touch upon a wide range of topics including paraconsistent logic, quantum logic, geometry of oppositions, categorical logic, computational logic, fundamental logic notions (identity, rule, quantification) and history of logic (Leibniz, Peirce, Hilbert). The volume gathers personal recollections about Jean-Yves Béziau and an autobiography, followed by 25 papers written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Irving Anellis, Dov Gabbay, Ivor Grattan-Guinness, Istvan Németi, Henri Prade. These essays will be of interest to all students and researchers interested in the nature and future of logic.

Universal Logic

This work conceptualizes a new logic, where the main inference connective is understood as meaning containment. Classical logic plays a restricted role, applying to classical sentences, while the new logic is studied in depth with chapters on semantics, proof theory, and properties. Based on this logic, simple consistency is proved for naive class theory, also in conjunction with classical theories such as a Z-F-style set theory. This book shows how the main set-theoretic and semantic paradoxes can be solved in a systematic way, which is conceptualized independently of the paradoxes themselves.