Sensible Semantics of Imperfect Information

On a Formal Feature of Meanings
  • Pietro Galliani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6521)


In [1] Cameron and Hodges proved, by means of a combinatorial argument, that no compositional semantics for a logic of Imperfect Information such as Independence Friendly Logic [2] or Dependence Logic ([3]) may use sets of tuples of elements as meanings of formulas.

However, Cameron and Hodges’ theorem fails if the domain of the semantics is restricted to infinite models only, and they conclude that

Common sense suggests that there is no sensible semantics for CS on infinite structures A , using subsets of the domain of A as interpretations for formulas with one free variable. But we don’t know a sensible theorem along these lines ([1]).

This work develops a formal, natural definition of “sensible semantics” according to which the statement quoted above can be proved.


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  1. 1.
    Cameron, P., Hodges, W.: Some Combinatorics of Imperfect Information. The Journal of Symbolic Logic 66(2), 673–684 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Hintikka, J.: The Principles of Mathematics Revisited. Cambridge University Press, Cambridge (1996)CrossRefzbMATHGoogle Scholar
  3. 3.
    Väänänen, J.: Dependence Logic. Cambridge University Press, Cambridge (2007)CrossRefzbMATHGoogle Scholar
  4. 4.
    Hodges, W.: Compositional Semantics for a Language of Imperfect Information. Journal of the Interest Group in Pure and Applied Logics 5 (4), 539–563 (1997)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Henkin, L.: Some Remarks on Infinitely Long Formulas. In: Infinitistic Methods. Proc. Symposium on Foundations of Mathematics, pp. 167–183. Pergamon Press, Oxford (1961)Google Scholar
  6. 6.
    Hintikka, J., Sandu, G.: Informational independence as a semantic phenomenon. In: Fenstad, J., Frolov, I., Hilpinen, R. (eds.) Logic, Methodology and Philosophy of Science, pp. 571–589. Elsevier, Amsterdam (1989)Google Scholar
  7. 7.
    Janssen, T.: Independent Choices and the Interpretation of IF Logic. Journal of Logic, Language and Information 11, 367–387 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Caicedo, X., Dechesne, F., Jannsen, T.: Equivalence and Quantifier Rules for Logic with Imperfect Information. Logic Journal of the IGPL 17(1), 91–129 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Hintikka, J., Sandu, G.: Game-Theoretical Semantics. In: van Benthem, J., Meulen, A.T. (eds.) Handbook of Logic and Language, pp. 361–410. Elsevier, Amsterdam (1997)CrossRefGoogle Scholar
  10. 10.
    Hodges, W.: Logics of imperfect information: why sets of assignments. In: van Benthem, J., Gabbay, D., Löwe, B. (eds.) Proceedings of 7th De Morgan Workshop ’Interactive Logic: Games and Social Software (2005)Google Scholar
  11. 11.
    Hodges, W.: Formal features of compositionality. Journal of Logic, Language, and Information 10(1), 7–28 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Janssen, T.: Compositionality. In: van Benthem, J., ter Meulen, A. (eds.) Handbook of Logic and Language, pp. 417–473. Elsevier, Amsterdam (1996)Google Scholar
  13. 13.
    Montague, R.: Universal grammar. Theoria 36, 373–398 (1970)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Pietro Galliani
    • 1
  1. 1.Institute for Logic, Language and ComputationUniversiteit van AmsterdamAmsterdamThe Netherlands

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