Theory of Graded Consequence - A General Framework for Logics of Uncertainty

This book introduces the theory of graded consequence (GCT) and its mathematical formulation. It also compares the notion of graded consequence with other notions of consequence in fuzzy logics, and discusses possible applications of the theory in approximate reasoning and decision-support systems. One of the main points where this book emphasizes on is that GCT maintains the distinction between the three different levels of languages of a logic, namely object language, metalanguage and metametalanguage, and thus avoids the problem of violation of the principle of use and mention; it also shows, gathering evidences from existing fuzzy logics, that the problem of category mistake may arise as a result of not maintaining distinction between levels.

List of contents

Introduction.- Basics of GCT.- Incorporating Negation in object language .- Proof theory for graded consequence.- Relationship with some other consequence operators and relations.- Suggested applications.

Summary

This book introduces the theory of graded consequence (GCT) and its mathematical formulation. It also compares the notion of graded consequence with other notions of consequence in fuzzy logics, and discusses possible applications of the theory in approximate reasoning and decision-support systems. One of the main points where this book emphasizes on is that GCT maintains the distinction between the three different levels of languages of a logic, namely object language, metalanguage and metametalanguage, and thus avoids the problem of violation of the principle of use and mention; it also shows, gathering evidences from existing fuzzy logics, that the problem of category mistake may arise as a result of not maintaining distinction between levels.

Product details

• Authors: Mihir Kuma Chakraborty, Mihir Kumar Chakraborty, Soma Dutta
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 01.01.2019
• EAN: 9789811388941
• ISBN: 978-981-1388-94-1
• No. of pages: 224
• Dimensions: 156 mm x 241 mm x 19 mm
• Weight: 516 g
• Illustrations: XIII, 224 p. 16 illus.
• Series: Logic in Asia: Studia Logica Library; Logic in Asia: Studia Logica L
• Subjects: Humanities, art, music > Philosophy > General, dictionaries; Non-fiction book > Philosophy, religion > Philosophy: general, reference works; B, Logic, mathematische Grundlagen, Mathematik: Logik, Religion and Philosophy, Mathematical logic, Mathematical Logic and Foundations, Mathematical foundations, many-valued logics, Residuated Lattices, Syntactic and Semantic Approaches