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Handbook of Philosophical Logic
The ninth volume of the Second Edition contains major contributions on Rewriting Logic as a Logical and Semantic Framework, Logical Frameworks, Proof Theory and Meaning, Goal Directed Deductions, Negations, Completeness and Consistency as well as Logic as General Rationality. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.
The Epistemic Lightness of Truth
This volume explores the deflationary claim of the innocence of truth, taking into account recent results on axiomatic truth theories.
Logic Colloquium '02
Logic Colloquium '02 includes articles from some of the world's preeminent logicians. The topics span all areas of mathematical logic, but with an emphasis on Computability Theory and Proof Theory. This book will be of interest to graduate students and researchers in the field of mathematical logic.
Logic, Language, Information, and Computation
Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 24th Workshop on Logic, Language, Information and Communication, WoLLIC 2017, held in London, UK, in August 2017. The 28 contributed papers were carefully reviewed and selected from 61 submissions. They cover interdisciplinary research in pure and applied logic, aiming at interactions between logic and the sciences related to information and computation.
Uncertain Reasoning in Justification Logic
This thesis studies the combination of two well known formal systems for knowledge representation: probabilistic logic and justification logic. Our aim is to design a formal framework that allows the analysis of epistemic situations with incomplete information. In order to achieve this we introduce two probabilistic justification logics, which are defined by adding probability operators to the minimal justification logic J. We prove soundness and completeness theorems for our logics and establish decidability procedures. Both our logics rely on an infinitary rule so that strong completeness can be achieved. One of the most interesting mathematical results for our logics is the fact that adding only one iteration of the probability operator to the justification logic J does not increase the computational complexity of the logic.
Logical Foundations of Computer Science
This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2018, held in Deerfield Beach, FL, USA, in January 2018. The 22 revised full papers were carefully reviewed and selected from 22 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verificati...
Proofs and Computations
Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.
Computational Logic and Proof Theory
This book constitutes the refereed proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory, KGC '97, held in Vienna, Austria, in August 1997. The volume presents 20 revised full papers selected from 38 submitted papers. Also included are seven invited contributions by leading experts in the area. The book documents interdisciplinary work done in the area of computer science and mathematical logics by combining research on provability, analysis of proofs, proof search, and complexity.
Introduction to the Theory of Schemes
This English edition of Yuri I. Manin's well-received lecture notes provides a concise but extremely lucid exposition of the basics of algebraic geometry and sheaf theory. The lectures were originally held in Moscow in the late 1960s, and the corresponding preprints were widely circulated among Russian mathematicians. This book will be of interest to students majoring in algebraic geometry and theoretical physics (high energy physics, solid body, astrophysics) as well as to researchers and scholars in these areas. "This is an excellent introduction to the basics of Grothendieck's theory of schemes; the very best first reading about the subject that I am aware of. I would heartily recommend every grad student who wants to study algebraic geometry to read it prior to reading more advanced textbooks."- Alexander Beilinson
