Logic The Theory Of Formal Inference
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Logic: The Theory of Formal Inference
Author: Alice Ambrose
language: en
Publisher: Courier Dover Publications
Release Date: 2015-11-04
Geared toward college undergraduates new to the subject, this concise introduction to formal logic was written by Alice Ambrose and Morris Lazerowitz, a pair of noted scholars and prolific authors in this field. A preliminary section opens the subject under the heading of truth-functions. Two subsequent parts on quantification and classes, each subdivided into numerous brief specifics, complete the overview. Suitable for students of philosophy as well as mathematics, the three-part treatment begins with the intuitive development of the standard theory of sentential connectives (called "operators"). The theory is further developed with the assistance of truth-tables and ultimately as a logistic system. Part II explores first-order quantification theory. In addition to examining most of the familiar laws that can be expressed by monadic formulas, the text addresses polyadic principles and the theories of identity and descriptions. Part III focuses on elementary concepts of classes, from class membership and class inclusion to the algebra of classes. Each part concludes with a series of exercises.
Mathematical Logic
Mathematical logic is a branch of mathematics that takes axiom systems and mathematical proofs as its objects of study. This book shows how it can also provide a foundation for the development of information science and technology. The first five chapters systematically present the core topics of classical mathematical logic, including the syntax and models of first-order languages, formal inference systems, computability and representability, and Gödel’s theorems. The last five chapters present extensions and developments of classical mathematical logic, particularly the concepts of version sequences of formal theories and their limits, the system of revision calculus, proschemes (formal descriptions of proof methods and strategies) and their properties, and the theory of inductive inference. All of these themes contribute to a formal theory of axiomatization and its application to the process of developing information technology and scientific theories. The book also describes the paradigm of three kinds of language environments for theories and it presents the basic properties required of a meta-language environment. Finally, the book brings these themes together by describing a workflow for scientific research in the information era in which formal methods, interactive software and human invention are all used to their advantage. The second edition of the book includes major revisions on the proof of the completeness theorem of the Gentzen system and new contents on the logic of scientific discovery, R-calculus without cut, and the operational semantics of program debugging. This book represents a valuable reference for graduate and undergraduate students and researchers in mathematics, information science and technology, and other relevant areas of natural sciences. Its first five chapters serve as an undergraduate text in mathematical logic and the last five chapters are addressed to graduate students in relevant disciplines.
An Introduction to the Theory of Formal Languages and Automata
Author: W. J. Levelt
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2019-03-18
No detailed description available for "An Introduction to the Theory of Formal Languages and Automata".