Analysis and Synthesis of Logics

How to Cut and Paste Reasoning Systems

  • Walter Carnielli
  • Marcelo Coniglio
  • Dov M. Gabbay
  • Paula Gouveia
  • Cristina Sernadas

Part of the Applied Logic Series book series (APLS, volume 35)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Walter Carnielli, Marcelo Coniglio, Dov M. Gabbay, Paula Gouveia, Cristina Sernadas
    Pages 1-36
  3. Walter Carnielli, Marcelo Coniglio, Dov M. Gabbay, Paula Gouveia, Cristina Sernadas
    Pages 37-89
  4. Walter Carnielli, Marcelo Coniglio, Dov M. Gabbay, Paula Gouveia, Cristina Sernadas
    Pages 91-137
  5. Walter Carnielli, Marcelo Coniglio, Dov M. Gabbay, Paula Gouveia, Cristina Sernadas
    Pages 139-178
  6. Walter Carnielli, Marcelo Coniglio, Dov M. Gabbay, Paula Gouveia, Cristina Sernadas
    Pages 179-214
  7. Walter Carnielli, Marcelo Coniglio, Dov M. Gabbay, Paula Gouveia, Cristina Sernadas
    Pages 215-261
  8. Walter Carnielli, Marcelo Coniglio, Dov M. Gabbay, Paula Gouveia, Cristina Sernadas
    Pages 263-322
  9. Walter Carnielli, Marcelo Coniglio, Dov M. Gabbay, Paula Gouveia, Cristina Sernadas
    Pages 323-388
  10. Walter Carnielli, Marcelo Coniglio, Dov M. Gabbay, Paula Gouveia, Cristina Sernadas
    Pages 389-433
  11. Walter Carnielli, Marcelo Coniglio, Dov M. Gabbay, Paula Gouveia, Cristina Sernadas
    Pages 435-518
  12. Walter Carnielli, Marcelo Coniglio, Dov M. Gabbay, Paula Gouveia, Cristina Sernadas
    Pages 519-558
  13. Back Matter
    Pages 559-600

About this book

Introduction

Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature (for instance, two Hilbert calculi or a Hilbert calculus and a tableau calculus). The important issue of preservation of properties is extensively addressed. For instance, sufficient conditions are provided for a combined logic to be sound and complete when the original component logics are known to be sound and complete.

The book brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). It also provides examples of potential applications in emergent fields like security protocols, quantum computing, networks and argumentation theory, besides discussing more classical applications like software specification, knowledge representation, computational linguistics and modular automated reasoning.

This monograph will be of interest to researchers and graduate students in mathematical logic, theory of computation and philosophical logic with no previous knowledge of the subject of combining and decomposing logics, but with a working knowledge of first-order logic. The book will also be relevant for people involved in research projects where logic is used as a tool and the need for working with several logics at the same time is mandatory (for instance, temporal, epistemic and probabilistic logics).

Keywords

Argumentation Theory Combination of logics Decomposition of logics Fibring of logics Network fibring Preservation of properties logic mathematical logic predicate logic

Authors and affiliations

  • Walter Carnielli
    • 1
  • Marcelo Coniglio
    • 2
  • Dov M. Gabbay
    • 3
  • Paula Gouveia
    • 4
  • Cristina Sernadas
    • 5
  1. 1.University of Campinas (UNICAMP)Brazil
  2. 2.University of Campinas (UNICAMP)Brazil
  3. 3.King’s CollegeLondonUnited Kingdom
  4. 4.Instituto Superior TecnicoLisbonPortugal
  5. 5.Instituto Superior TecnicoLisbonPortugal

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4020-6782-2
  • Copyright Information Springer Science+Business Media B.V. 2008
  • Publisher Name Springer, Dordrecht
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4020-6781-5
  • Online ISBN 978-1-4020-6782-2
  • Series Print ISSN 1386-2790
  • About this book