Skip to main content
SpringerLink
Log in
Book cover

Games: Unifying Logic, Language, and Philosophy pp 249–350Cite as

In the Beginning was Game Semantics?

  • Chapter

Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 15))

Abstract

This chapter presents an overview of computability logic—the game-semantically constructed logic of interactive computational tasks and resources. There is only one non-overview, technical section in it, devoted to a proof of the soundness of affine logic with respect to the semantics of computability logic.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Abramsky, S. and Jagadeesan, R. (1994). Games and full completeness for multiplicative linear logic. Journal of Symbolic Logic, 59(2):543–574.

    Article  Google Scholar 

  • Blass, A. (1972). Degrees of indeterminacy of games. Fundamenta Mathematicæ, 77:151–166.

    Google Scholar 

  • Blass, A. (1992). A game semantics for linear logic. Annals of Pure and Applied Logic, 56: 183–220.

    Article  Google Scholar 

  • Felscher, W. (1985). Dialogues, strategies, and intuitionistic provability. Annals of Pure and Applied Logic, 28:217–254.

    Article  Google Scholar 

  • Girard, J.Y. (1987). Linear logic. Theoretical Computer Science, 50(1):1–102.

    Article  Google Scholar 

  • Gödel, K. (1958). ü ber eine bisher noch nicht benützte Erweiterung des finiten Standpunktes. Dialectica, 12:280–287.

    Article  Google Scholar 

  • Goldin, D. Q., Smolka, S. A., Attie, P. C., and Sonderegger, E. L. (2004). Turing machines, transition systems, and interaction. Information and Computation, 194(2):101–128.

    Article  Google Scholar 

  • Japaridze, G. (1997). A constructive game semantics for the language of linear logic. Annals of Pure and Applied Logic, 85:87–156.

    Article  Google Scholar 

  • Japaridze, G. (2000). The propositional logic of elementary tasks. Notre Dame Journal of Formal Logic, 41(2):171–183.

    Article  Google Scholar 

  • Japaridze, G. (2002). The logic of tasks. Annals of Pure and Applied Logic, 117:263–295.

    Article  Google Scholar 

  • Japaridze, G. (2003). Introduction to computability logic. Annals of Pure and Applied Logic, 123:1–99.

    Article  Google Scholar 

  • Japaridze, G. (2006a). From truth to computability I. Theoretical Computer Science, 357:100–135.

    Article  Google Scholar 

  • Japaridze, G. (2006b). Introduction to cirquent calculus and abstract resource semantics. Journal of Logic and Computation, 16(4):489–532.

    Article  Google Scholar 

  • Japaridze, G. (2006c). Propositional computability logic I. ACM Transactions on Computational Logic, 7(2):302–330.

    Article  Google Scholar 

  • Japaridze, G. (2006d). Propositional computability logic II. ACM Transactions on Computational Logic, 7(2):331–362.

    Article  Google Scholar 

  • Japaridze, G. (2006e). Computability logic: a formal theory of interaction. In Goldin, D., Smolka, S., and Wegner, P., editors, Interactive Computation: The New Paradigm. pages 183–223. Springer, Berlin.

    Google Scholar 

  • Japaridze, G. (2007a). From truth to computability II. Theoretical Computer Science, 379:20–52.

    Article  Google Scholar 

  • Japaridze, G. (2007b). Intuitionistic computability logic. Acta Cybernetica, 18(1):77–113.

    Google Scholar 

  • Japaridze, G. (2007c). The logic of interactive Turing reduction. Journal of Symbolic Logic, 72(1):243–276.

    Article  Google Scholar 

  • Japaridze, G. (2007d). The intuitionistic fragment of computability logic at the propositional level. Annals of Pure and Applied Logic, 147(3):187–227.

    Article  Google Scholar 

  • Japaridze, G. (2008a). Cirquent calculus deepened. Journal of Logic and Computation,18(6):983–1028.

    Article  Google Scholar 

  • Japaridze, G. (2008b). Sequential operators in computability logic. Information and Computation, 206(12):1443–1475.

    Article  Google Scholar 

  • Japaridze, G. (2009). Many concepts and two logics of algorithmic reduction. Studia Logica, 91 (to appear).

    Google Scholar 

  • Kleene, S.C. (1952). Introduction to Metamathematics. D. van Nostrand Company, New Yo r k /Toronto.

    Google Scholar 

  • Kolmogorov, A.N. (1932). Zur Deutung der intuitionistischen Logik. Mathematische Zeitschrift, 35:58–65.

    Article  Google Scholar 

  • Konolige, K. (1988). On the relation between default and autoepistemic logic. Artificial Intelligence, 35(3):343–382.

    Article  Google Scholar 

  • Levesque, H. and Lakemeyer, G. (2000). The Logic of Knowledge Bases. MIT Press, Cambridge, MA.

    Google Scholar 

  • Lorenzen, P. (1959). Ein dialogisches Konstruktivitätskriterium. In Infinitistic Methods, pages 193–200. PWN, Warsaw.

    Google Scholar 

  • Milner, R. (1993). Elements of interaction. Communications of the ACM, 36(1):79–89.

    Article  Google Scholar 

  • Moore, R. (1985). A formal theory of knowledge and action. In Hobbs, J. and Moore, R., editors, Formal Theories of Commonsense Worlds. Ablex, Norwood, NJ.

    Google Scholar 

  • Pietarinen, A. (2002). Semantic Games in Logic and Language. Academic dissertation, University of Helsinki, Helsinki.

    Google Scholar 

  • Sipser, M. (2006). Introduction to the Theory of Computation. Thomson Course Technology, USA, 2nd edition.

    Google Scholar 

  • Turing, A. (1936). On computable numbers with an application to the entsheidungsproblem. Proceedings of the London Mathematical Society, 42(2):230–265.

    Google Scholar 

  • van Benthem, J. (2001). Logic in games. ILLC preprint, University of Amsterdam, Amsterdam.

    Google Scholar 

  • Vereshchagin, N. (2006) Japaridze's computability logic and intuitionistic propositional calculus. Moscow State University Preprint, 2006. http://lpcs.math.msu.su/?ver/papers/japaridze.ps.

  • Wegner, P. (1998). Interactive foundations of computing. Theoretical Computer Science,192:315–351.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computing Sciences, Villanova University, 800 Lancaster Avenue, Villanova, Pennsylvania, 19085, USA

    Giorgi Japaridze

Authors
  1. Giorgi Japaridze
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Academy of Sciences of the Czech Republic Institute of Philosophy, Jilska 1, Prague 1, 110 00, Czech Republic

    Ondrej Majer

  2. Department of Philosophy, University of Helsinki, Siltavuorenpenger 20 A, P.O. Box 9, Helsinki, FI-00014, Finland

    Ahti-Veikko Pietarinen  & Tero Tulenheimo  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science + Business Media B.V.

About this chapter

Cite this chapter

Japaridze, G. (2009). In the Beginning was Game Semantics?. In: Majer, O., Pietarinen, AV., Tulenheimo, T. (eds) Games: Unifying Logic, Language, and Philosophy. Logic, Epistemology, and the Unity of Science, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9374-6_11

Download citation

Publish with us

Policies and ethics

Search

Navigation