Perspectives In Logic
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Proofs and Computations
Author: Helmut Schwichtenberg
language: en
Publisher: Cambridge University Press
Release Date: 2011-12-15
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.
Model-Theoretic Logics
Author: J. Barwise
language: en
Publisher: Cambridge University Press
Release Date: 2017-03-02
This book brings together several directions of work in model theory between the late 1950s and early 1980s.
Reasoning, Necessity, and Logic
Author: Willis F. Overton
language: en
Publisher: Psychology Press
Release Date: 2013-05-13
A presentation of current work that systematically explores and articulates the nature, origin and development of reasoning, this volume's primary aim is to describe and examine contemporary theory and research findings on the topic of deductive reasoning. Many contributors believe concepts such as "structure," "competence," and "mental logic" are necessary features for a complete understanding of reasoning. As the book emanates from a Jean Piaget Symposium, his theory of intellectual development as the standard contemporary treatment of deductive reasoning is used as the context in which the contributors elaborate on their own perceptions.