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Volume 153. Quantification in Nonclassical Logic

Published: 9th June 2009 Authors: Dov M. Gabbay Dimitrij Skvortsov Valentin Shehtman
Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy and language in ancient times; they were studied by traditional informal methods until the 20th century. In the last century the tools became highly mathematical, and both modal logic and quantification found numerous applications in Computer Science. At the same time many other kinds of nonclassical logics were investigated and applied to Computer Science. Although there exist several good books in propositional modal logics, this book is the first detailed monograph in nonclassical first-order quantification. It includes results obtained during the past thirty years. The field is very large, so we confine ourselves with only two kinds of logics: modal and superintuitionistic. The main emphasis of Volume 1 is model-theoretic, and it concentrates on descriptions of different sound semantics and completeness problem --- even for these seemingly simple questions we have our hands full. The major part of the presented material has never been published before. Some results are very recent, and for other results we either give new proofs or first proofs in full detail.

Additional volumes


Volume 152. Realizability

Published: 6th March 2008 Author: Jaap van Oosten

Volume 151. Residuated Lattices: An Algebraic Glimpse at Substructural Logics

Published: 25th April 2007 Authors: Nikolaos Galatos Peter Jipsen Tomasz Kowalski Hiroakira Ono

Volume 150. Relation Algebras

Published: 15th May 2006 Author: Roger Maddux

Volume 149. Lectures on the Curry-Howard Isomorphism

Published: 4th July 2006 Authors: Morten Heine Sørensen Pawel Urzyczyn

Volume 148. Many-Dimensional Modal Logics: Theory and Applications

Published: 21st October 2003 Authors: A. Kurucz F. Wolter M. Zakharyaschev Dov M. Gabbay

Volume 147. Relation Algebras by Games

Published: 15th August 2002 Authors: Robin Hirsch Ian Hodkinson

Volume 146. Rudiments of Calculus

Published: 7th February 2001 Editors: A. Arnold D. Niwinski

Volume 145. Theory of Relations

Published: 15th December 2000 Author: R. Fraisse

Volume 144. Computable Structures and the Hyperarithmetical Hierarchy

Published: 16th June 2000 Authors: C.J. Ash J. Knight

Volume 143. Classical Recursion Theory, Volume II

Published: 7th September 1999 Author: P. Odifreddi

Volume 142. Tools and Techniques in Modal Logic

Published: 17th June 1999 Author: M. Kracht

Volume 141. Categorical Logic and Type Theory

Published: 14th January 1999 Author: B. Jacobs

Volume 140. Handbook of Computability Theory

Published: 1st October 1999 Editor: E.R. Griffor

Volume 137. Handbook of Proof Theory

Published: 9th July 1998 Editor: S.R. Buss

Volume 136. Admissibility of Logical Inference Rules

Published: 14th March 1997 Author: V.V. Rybakov

Volume 135. Logical Frameworks for Truth and Abstraction

Published: 14th March 1996 Author: A. Cantini

Volume 134. Logic, Methodology and Philosophy of Science IX

Published: 10th January 1995 Editors: D. Prawitz B. Skyrms D. Westerståhl

Volume 133. Selected Papers on Automath

Published: 20th October 1994 Editors: R.P. Nederpelt J.H. Geuvers R.C. de Vrijer

Volume 132. Hausdorff Gaps and Limits

Published: 23rd February 1994 Authors: R. Frankiewicz P. Zbierski

Volume 131. Recursive Functionals

Published: 18th May 1992 Author: L.E. Sanchis

Volume 130. Language in Action

Published: 12th February 1991 Author: J. van Benthem

Volume 129. Logic Colloquium '87

Published: 1st August 1989 Editors: H.-D. Ebbinghaus J. Fernandez-Prida M. Garrido D. Lascar M. Rodriguez Artalejo

Volume 128. Computability, Complexity, Logic

Published: 1st July 1989 Author: E. Börger

Volume 127. Logic Colloquium '88

Published: 4th August 1989 Editors: R. Ferro C. Bonotto S. Valentini A. Zanardo

Volume 126. Logic, Methodology and Philosophy of Science VIII

Published: 16th August 1989 Editors: J.E. Fenstad I.T. Frolov R. Hilpinen

Volume 125. Classical Recursion Theory

Published: 4th February 1992 Author: P. Odifreddi

Volume 124. Logic Colloquium '86

Published: 1st November 1987 Editors: F.R. Drake J.K. Truss

Volume 123. Constructivism in Mathematics, Vol 2

Published: 1st November 1988 Authors: A.S. Troelstra D. van Dalen

Volume 121. Constructivism in Mathematics

Published: 1st August 1988 Editors: J. Barwise D. Kaplan H.J. Keisler Authors: A.S. Troelstra D. Van Dalen

Volume 121. Constructivism in Mathematics, Vol 1

Published: 1st July 1988 Authors: A.S. Troelstra D. van Dalen

Logic Colloquium '85

Published: 1st January 1987 Editor: The Paris Logic Group

Volume 117. Harvey Friedman's Research on the Foundations of Mathematics

Published: 1st November 1985 Editors: L.A. Harrington M.D. Morley A. Šcedrov S.G. Simpson

Volume 116. Equivalents of the Axiom of Choice, II

Published: 1st March 1985 Authors: H. Rubin J.E. Rubin

Volume 115. Cylindric Algebras

Published: 1st February 1985 Author: Author Unknown

Volume 114. Logic, Methodology and Philosophy of Science VII

Published: 1st May 1986 Editors: R. Barcan Marcus G.J.W. Dorn P. Weingartner

Volume 113. Intensional Mathematics

Published: 1st January 1985 Editor: S. Shapiro

Volume 112. Logic Colloquium '82

Published: 1st January 1984 Editors: G. Lolli G. Longo A. Marcja

Volume 110. The L.E.J. Brouwer Centenary Symposium

Published: 1st January 1982 Editors: A.S. Troelstra D. van Dalen

Volume 106. Combinatorial Set Theory: Partition Relations for Cardinals

Published: 1st May 1984 Authors: P. Erdös A. Máté A. Hajnal P. Rado

Volume 103. The Lambda Calculus

Published: 1st October 1984 Author: H.P. Barendregt

Volume 102. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 102. Set Theory An Introduction To Independence Proofs

Published: 1st December 1983 Author: K. Kunen

Volume 100. Descriptive Set Theory

Published: 1st January 1987 Author: Y.N. Moschovakis

Volume 99. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 97. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 96. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 95. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 94. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 93B. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 93A. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 92. Classification Theory

Published: 6th December 1990 Author: S. Shelah

Volume 91. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 90. Handbook of Mathematical Logic

Published: 1st March 1982 Editor: J. Barwise

Volume 89. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 88. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 87. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 86. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 85. Boole's Logic and Probability

Published: 1st October 1986 Author: T. Hailperin

Volume 84. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 83. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 82. Proceedings of the Third Scandinavian Logic Symposium

Published: 1st August 1975 Editor: Stig Kanger

Volume 81. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 80. Logic Colloquium '73: Proceedings of the Logic Colloquium

Published: 1st January 1975 Editors: H. E. Rose J. C. SHEPHERDSON

Volume 79. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 78. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 77. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 76. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 75. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 74. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 73. Model Theory

Published: 12th June 1990 Authors: C.C. Chang H.J. Keisler

Volume 72. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 71. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 70. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 69. Contributions to Non-Standard Analysis

Published: 1st April 2000 Author: Lev Beklemishev

Volume 68. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 67. Foundations of Set Theory

Published: 1st December 1973 Authors: A.A. Fraenkel Y. Bar-Hillel A. Levy

Volume 66. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 65. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 63. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 62. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 61. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 60. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 59. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 57. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 56. Constructive Order Types

Published: 1st April 2000 Author: Lev Beklemishev

Volume 55. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 54. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 53. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 52. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 51. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 50. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 49. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 48. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 47. Problems in the Philosophy of Mathematics

Published: 1st January 1967 Editor: Brouwer

Volume 46. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 45. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 44. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 43. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 42. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 41. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 40. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 39. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 38. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 37. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 36. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 35. Computer Programming and Formal Systems

Published: 1st April 2000 Author: Lev Beklemishev

Volume 34. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 33. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 32. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 31. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 30. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 29. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 28. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 27. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 26. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 25. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 24. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 23. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 22. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 21. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 20. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 19. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 18. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 17. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 16. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 15. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 14. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 13. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 12. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 11. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 10. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 7. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 5. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 4. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 3. Provability, Computability and Reflection

Published: 1st April 2000 Author: Lev Beklemishev

Volume 2. Spectral Theory of Random Matrices

Author: Vyacheslav Girko

Volume 2. Recursive Algebra, Analysis and Combinatorics

Published: 30th November 1998 Author: Author Unknown

Volume 1. Spectral Theory of Random Matrices

Published: 1st April 2000 Author: Vyacheslav Girko

Volume 1. Recursive Model Theory

Published: 30th November 1998 Author: Author Unknown

Topoi

Published: 1st February 1984 Author: R. Goldblatt

Volume .. Proceedings of the Herbrand Symposium

Published: 12th February 1982 Editor: J. Stern