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Ordinal Analysis with an Introduction to Proof Theory
This book provides readers with a guide to both ordinal analysis, and to proof theory. It mainly focuses on ordinal analysis, a research topic in proof theory that is concerned with the ordinal theoretic content of formal theories. However, the book also addresses ordinal analysis and basic materials in proof theory of first-order or omega logic, presenting some new results and new proofs of known ones.Primarily intended for graduate students and researchers in mathematics, especially in mathematical logic, the book also includes numerous exercises and answers for selected exercises, designed to help readers grasp and apply the main results and techniques discussed.
Advances in Mathematical Logic
Gaisi Takeuti was one of the most brilliant, genius, and influential logicians of the 20th century. He was a long-time professor and professor emeritus of mathematics at the University of Illinois at Urbana-Champaign, USA, before he passed away on May 10, 2017, at the age of 91. Takeuti was one of the founders of Proof Theory, a branch of mathematical logic that originated from Hilbert's program about the consistency of mathematics. Based on Gentzen's pioneering works of proof theory in the 1930s, he proposed a conjecture in 1953 concerning the essential nature of formal proofs of higher-order logic now known as Takeuti's fundamental conjecture and of which he gave a partial positive solu...
Sets and Proofs
First of two volumes providing a comprehensive guide to mathematical logic.
Proceedings Of The 10th Asian Logic Conference
The 10th Asian Logic Conference is part of the series of logic conferences inaugurated in Singapore in 1981. This meeting is held every three years and rotates among countries in the Asia-Pacific region, with interests in the broad area of logic, including theoretical computer science. It is now considered a major conference in this field and is regularly sponsored by the Association of Symbolic Logic.This volume contains papers from the 10th meeting held in Kobe, Japan.
Proceedings Of The 11th Asian Logic Conference: In Honor Of Professor Chong Chitat On His 60th Birthday
The Asian Logic Conference is part of the series of logic conferences inaugurated in Singapore in 1981. It is normally held every three years and rotates among countries in the Asia-Pacific region. The 11th Asian Logic Conference was held at the National University of Singapore, in honor of Professor Chong Chitat on the occasion of his 60th birthday. The conference is on the broad area of logic, including theoretical computer science. It is considered a major event in this field and is regularly sponsored by the Association of Symbolic Logic. This volume contains papers from this meeting.
Proceedings of the 10th Asian Logic Conference, Kobe, Japan, 1-6 September 2008
The 10th Asian Logic Conference is part of the series of logic conferences inaugurated in Singapore in 1981. This meeting is held every three years and rotates among countries in the Asia-Pacific region, with interests in the broad area of logic, including theoretical computer science. It is now considered a major conference in this field and is regularly sponsored by the Association of Symbolic Logic. This volume contains papers from the 10th meeting held in Kobe, Japan.
Nonclassical Logics and Their Applications
This edited book focuses on non-classical logics and their applications, highlighting the rapid advances and the new perspectives that are emerging in this area. Non-classical logics are logical formalisms that violate or go beyond classical logic laws, and their specific features make them particularly suited to describing and reason about aspects of social interaction. The richness and diversity of non-classical logics mean that this area is a natural catalyst for ideas and insights from many different fields, from information theory to game theory and business science. This volume is the post-proceedings of the 8th International Conference on Logic and Cognition, held at Sun Yat-Sen Unive...
Logic, Language, Information and Computation
Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the 4th volume of the FoLLI LNAI subline; containing the refereed proceedings of the 16h International Workshop on Logic, Language, Information and Computation, WoLLIC 2009, held in Tokyo, Japan, in June 2009. The 25 revised full papers presented together with six tutorials and invited talks were carefully reviewed and selected from 57 submissions. The papers cover some of the most active areas of research on the frontiers between computation, logic, and linguistics, with particular interest in cross-disciplinary topics. Typical areas of interest are: foundations of computing and programming; novel computation models and paradigms; broad notions of proof and belief; formal methods in software and hardware development; logical approach to natural language and reasoning; logics of programs, actions and resources; foundational aspects of information organization, search, flow, sharing, and protection.
Structures and Norms in Science
This book gives a state-of-the-art survey of current research in logic and philosophy of science, as viewed by invited speakers selected by the most prestigious international organization in the field. In particular, it gives a coherent picture of foundational research into the various sciences, both natural and social. In addition, it has special interest items such as symposia on interfaces between logic and methodology, semantics and semiotics, as well as updates on the current state of the field in Eastern Europe and the Far East.
The Legacy of Kurt Schütte
This book on proof theory centers around the legacy of Kurt Schütte and its current impact on the subject. Schütte was the last doctoral student of David Hilbert who was the first to see that proofs can be viewed as structured mathematical objects amenable to investigation by mathematical methods (metamathematics). Schütte inaugurated the important paradigm shift from finite proofs to infinite proofs and developed the mathematical tools for their analysis. Infinitary proof theory flourished in his hands in the 1960s, culminating in the famous bound Γ0 for the limit of predicative mathematics (a fame shared with Feferman). Later his interests shifted to developing infinite proof calculi f...
