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.

Suggests a general scheme for logic of uncertainty Outlines the philosophical grounds for use and mention of a symbol Analyses the metatheory of logic with its distinctive language and interpretation Presents different logics based on user's choice Provides a mathematical model applicable to decision-support systems and approximate reasoning

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