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## Über dieses Buch

This book is written as an introduction to annotated logics. It provides logical foundations for annotated logics, discusses some interesting applications of these logics and also includes the authors' contributions to annotated logics. The central idea of the book is to show how annotated logic can be applied as a tool to solve problems of technology and of applied science. The book will be of interest to pure and applied logicians, philosophers and computer scientists as a monograph on a kind of paraconsistent logic. But, the layman will also take profit from its reading.

## Inhaltsverzeichnis

### Chapter 1. Introduction

Abstract
This chapter gives motivations and the history of annotated logics as an introduction to this book. First, we discuss the importance of annotated logics in connection with paraconsistent logics. Second, we present the history of annotated logics by reviewing the literature on the subject.
Jair Minoro Abe, Seiki Akama, Kazumi Nakamatsu

### Chapter 2. Propositional Annotated Logics $$P\tau$$ P τ

Abstract
This chapter introduces the propositional annotated logics $$P\tau$$. We present a Hilbert style axiomatization of $$P\tau$$ and their semantics. We show some formal results including completeness.
Jair Minoro Abe, Seiki Akama, Kazumi Nakamatsu

### Chapter 3. Predicate Annotated Logics $$Q\tau$$ Q τ

Abstract
This chapter studies the predicate annotated logics $$Q\tau$$, which can be seen as a predicate extension of $$P\tau$$. Their axiomatization and semantics are considered. We also prove completeness and other metatheorems.
Jair Minoro Abe, Seiki Akama, Kazumi Nakamatsu

### Chapter 4. Formal Issues

Abstract
This chapter discusses formal issues of annotated logics. We describe an algebraic semantics for $$P\tau$$ based on Curry algebras. We also discuss annotated set theory, annotated model theory, proof methods, and annotated modal logics.
Jair Minoro Abe, Seiki Akama, Kazumi Nakamatsu

### Chapter 5. Variants and Related Systems

Abstract
This chapter reviews some variants of annotated logics and related systems in the literature. Variants include fuzzy annotated logics, possibilistic annotated logics, inductive annotated logics, and structural annotated logics. We also compare annotated logics with related systems such as Labelled Deductive Systems and General Logics. Finally, we review systems of paraconsistent logics.
Jair Minoro Abe, Seiki Akama, Kazumi Nakamatsu

### Chapter 6. Applications

Abstract
This chapter discusses applications of annotated logics for various areas. After reviewing paraconsistent logic programming and generalized annotated logic programming, we survey promising applications to knowledge representation, neural computing, automation and robotics.
Jair Minoro Abe, Seiki Akama, Kazumi Nakamatsu

### Chapter 7. Conclusions

Abstract
This chapter gives some conclusions with the summary of the book. It is possible to conclude that annotated logics are very interesting theoretically as well as practically. However, there are some future problems to be worked out.
Jair Minoro Abe, Seiki Akama, Kazumi Nakamatsu

### Backmatter

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