Dual Tableaux: Foundations, Methodology, Case Studies

ISBN-13: 9789400700048 / Angielski / Twarda / 2010 / 523 str.

Ewa Orlowska; Joanna Goli?ska-Pilarek

Opis

Providing a reference for researchers and students, this volume presents the fundamental concepts of dual tableaux, and a wide scope of applications. These include logic methods used in mathematics and philosophy, as well as applied theories of computational logic.

Recenzje

From the reviews:

"This book is an excellent guide for a unified treatment of the many logics surveyed ... . this book unifies a collection of topics and systems that are hard to find elsewhere, and testifies to the increasing interest in non-classical logic. ... Overall, it is undoubtedly a book to have in your library." (Walter Carnielli, Studia Logica, Vol. 101, 2013)

"This book surveys the theory and applications of the method of dual tableaux introduced by Rasiowa and Sikorski in the 1960s. A broad range of theories have been studied using this framework, and most of them are included here. ... Overall, the book introduces a thorough and in-depth study of the different applications of the framework of dual tableaux." (Manuel Ojeda-Aciego, Mathematical Reviews, Issue 2012 f)

"Providing a reference for researchers and students, this book presents the fundamental concepts of dual tableaux and a wide scope of applications. These include logic methods used in mathematics and philosophy as well as applied theories of computational logic." (Branislav Boricic, Zentralblatt MATH, Vol. 1210, 2011)

Spis treści

1. Dual Tableau for Classical First-Order Logic.- 2. Dual Tableaux for Logics of Classical Algebras of Binary.- 3. Theories of Point Relations and Relational Model Checking .- 4. Dual Tableaux for Peirce Algebras.- 5. Dual Tableaux for Fork Algebras .- 6. Dual Tableaux for Relational Databases .- Part III. Relational Reasoning in Traditional Non-classical Logics.- 7. Dual Tableaux for Classical Modal Logics.- 8. Dual Tableaux for Some Logics Based on Intuitionism.- 9. Dual Tableaux for Relevant Logics.- 10. Dual Tableaux for Many-valued Logics.- Part IV. Relational Reasoning in Logics of Information and Data.- Analysis.- 11. Dual Tableaux for Information Logics of Plain Frames .- 12. Dual Tableaux for Information Logics of Relative Frames.- 13. Dual Tableau for Formal Concept Analysis.- 14. Dual Tableau for a Fuzzy Logic.- 15. Dual Tableaux for Logics of Order of Magnitude Reasoning.- Part V. Relational Reasoning about Time, Space, and Action.- 16. Dual Tableaux for Temporal Logics.- 17. Dual Tableaux for Interval Temporal Logics.- 18. Dual Tableaux for Spatial Reasoning.- 19. Dual Tableaux for Logics of Programs .- Part VI. Beyond Relational Theories.- 20. Dual Tableaux for Threshold Logics.- 21. Signed Dual Tableau for G¨odel-Dummett Logic.- 22. Dual Tableaux for First-Order Post Logics.- 23. Dual Tableau for Propositional Logic with Identity.- 24. Dual Tableaux for Logics of Conditional Decisions.- 25. Methodological Principles of Dual Tableaux.- References.- Index.

Blurb

The book presents logical foundations of dual tableaux together with a number of their applications both to logics traditionally dealt with in mathematics and philosophy (such as modal, intuitionistic, relevant, and many-valued logics) and to various applied theories of computational logic (such as temporal reasoning, spatial reasoning, fuzzy-set-based reasoning, rough-set-based reasoning, order-of magnitude reasoning, reasoning about programs, threshold logics, logics of conditional decisions). The distinguishing feature of most of these applications is that the corresponding dual tableaux are built in a relational language which provides useful means of presentation of the theories. In this way modularity of dual tableaux is ensured. We do not need to develop and implement each dual tableau from scratch, we should only extend the relational core common to many theories with the rules specific for a particular theory.