Computability Logic: A Formal Theory of Interaction

  • Giorgi Japaridze


Generalizing the traditional concepts of predicates and their truth to interactive computational problems and their effective solvability, computability logic conservatively extends classical logic to a formal theory that provides a systematic answer to the question of what and how can be computed, just as traditional logic is a systematic tool for telling what is true. The present chapter contains a comprehensive yet relatively compact overview of this very recently introduced framework and research program. It is written in a semitutorial style with general computer science, logic and mathematics audiences in mind.


Formal Theory Turing Machine Classical Logic Legal Move Static Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. van Benthem. Logic in Games. Lecture Notes, Institute for Logic, Language and Computation (ILLC), University of Amsterdam, 2001.Google Scholar
  2. 2.
    A. Blass. A game semantics for linear logic. Ann Pure Appl Logic 56:183–220, 1992.zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    J. Girard. Linear logic. Theoret Comp Sci 50:1–102, 1987.zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    D. Goldin. Persistent Turing machines as a model of interactive computation. Lecture Notes in Comp Sci 1762:116–135, 2000.zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    D. Goldin, S. Smolka, P. Attie, E. Sonderegger. Turing machines, transition systems and interaction. Information and Computation 194:101–128, 2004.zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    G. Japaridze. Introduction to computability logic. Ann Pure Appl Logic 123:1–99, 2003.zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    G. Japaridze. Propositional computability logic I–II. ACM Transactions on Computational Logic 7:202–262, 2006.Google Scholar
  8. 8.
    G. Japaridze. From truth to computability I. Theoret Comp Sci 357:100–135, 2006.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    G. Japaridze. From truth to computability II., 2005.Google Scholar
  10. 10.
    G. Japaridze. Intuitionistic computability logic. Acta Cybernetica (to appear).Google Scholar
  11. 11.
    K. Konolige. On the relation between default and autoepistemic logic. In: Proceedings of the International Joint Conference on Artificial Intelligence. Detroit, MI, 1989.Google Scholar
  12. 12.
    R. Milner. Elements of interaction. Communications of the ACM 36:79–89, 1993.CrossRefGoogle Scholar
  13. 13.
    R. Moore. A formal theory of knowledge and action. In: Hobbs J, Moore R (eds.) Formal Theories of Commonsense Worlds. Ablex, Norwood, N.J., 1985.Google Scholar
  14. 14.
    M. Sipser. Introduction to the Theory of Computation, 2nd Edition. Thomson Course Technology, Boston, MA, 2006.Google Scholar
  15. 15.
    A. Turing. On Computable numbers with an application to the entsheidungsproblem. Proc London Math Soc 2.42:230–265, 1936.zbMATHGoogle Scholar
  16. 16.
    P. Wegner. Interactive foundations of computing. Theoret Comp Sci 192:315–351, 1998.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Giorgi Japaridze
    • 1
  1. 1.Villanova UniversityVillanovaUSA

Personalised recommendations