Studia Logica

, Volume 49, Issue 4, pp 523–539 | Cite as

A general possible worlds framework for reasoning about knowledge and belief

  • Heinrich Wansing


In this paper non-normal worlds semantics is presented as a basic, general, and unifying approach to epistemic logic. The semantical framework of non-normal worlds is compared to the model theories of several logics for knowledge and belief that were recently developed in Artificial Intelligence (AI). It is shown that every model for implicit and explicit belief (Levesque), for awareness, general awareness, and local reasoning (Fagin and Halpern), and for awareness and principles (van der Hoek and Meyer) induces a non-normal worlds model validating precisely the same formulas (of the language in question).


Artificial Intelligence Mathematical Logic Model Theory Unify Approach Computational Linguistic 
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. [Ba]
    J. Barwise, The Situation in Logic — IV: On the Model Theory of Common Knowledge, Center for the Study of Language and Information, Report No. CSLI-88-122, Stanford, 1988.Google Scholar
  2. [vB]
    J. F. A. K. van Benthem, Correspondence theory, in [GG], vol. II, 1984, pp. 167–247.Google Scholar
  3. [Ca]
    R. Carnap, Meaning and Necessity, Chicago University Press, 1947.Google Scholar
  4. [Ch]
    B. F. Chellas, Modal Logic: An Introduction, Cambridge University Press, 1980.Google Scholar
  5. [Cr1]
    M. J. Cresswell, Intensional logics and logical truth, Journal of Philosophical Logic 1 (1972), pp. 2–15.Google Scholar
  6. [Cr2]
    M. J. Cresswell, Hyperintensional logic, Studia Logica 34 (1975), pp. 25–38.Google Scholar
  7. [Du]
    J. M. Dunn, Relevance logic and entailment, in [GG], vol. III, 1986, pp. 117–224.Google Scholar
  8. [FH]
    R. Fagin and J. Y. Halpern, Belief, awareness, and limited reasoning, Artificial Intelligence 34 (1988), pp. 39–76.Google Scholar
  9. [GG]
    D. Gabbay and F. Guentner (eds.), Handbook of Philosophical Logic, vols. I–IV, Reidel, Dordrecht, 1984–1989.Google Scholar
  10. [Ha1]
    J. Y. Halpern, Reasoning about knowledge: An overview, in [Ha2], pp. 1–17.Google Scholar
  11. [Ha2]
    J. Y. Halpern (ed.), Theoretical Aspects of Reasoning about Knowledge: Proceedings of the 1986 Conference, Morgan Kaufmann, Los Altos, 1986.Google Scholar
  12. [Hi1]
    J. Hintikka, Knowledge and Belief: An Introduction to the Logic of the Two Notions, Cornell University Press, 1962.Google Scholar
  13. [Hi2]
    J. Hintikka, Impossible possible worlds vindicated, Journal of Philosophical Logic 4 (1975), pp. 475–484.Google Scholar
  14. [vdHM]
    W. van der Hoek and J.-J Ch. Meyer, Possible logics for belief, Rapport IR-170, Vrije Universiteit Amsterdam, 1988.Google Scholar
  15. [Ko]
    K. Konolige, What awareness isn't: A sentential view of implicit and explicit belief, in [Ha2], pp. 241–250.Google Scholar
  16. [Le]
    H. J. Levesque, A logic of implicit and explicit belief, Proceedings AAAI-84, Austin, Texas, 1984, pp. 198–202.Google Scholar
  17. [NS]
    I. Niiniluoto and E. Saarinen (eds.), Intensional Logic: Theory and Applications (Acta Philosophica Fennica 35), Helsinki, 1982.Google Scholar
  18. [Pa]
    R. Parikh, Knowledge and the problem of logical omniscience, in [RZ], pp. 432–439.Google Scholar
  19. [PW]
    D. Pearce and H. Wansing, On the methodology of possible worlds semantics, II: Non-normal worlds and propositional attitudes, Berichte der Gruppe für Logik, Wissens-theorie und Information, Freie Universität Berlin, Bericht 2/89, 1989, forthcoming in Acta Philosophica Fennica.Google Scholar
  20. [Ra1]
    V. Rantala, Impossible worlds semantics and logical omniscience, in [NS], pp. 106–115.Google Scholar
  21. [Ra2]
    V. Rantala, Quantified modal logic: Non-normal worlds and propositional attitudes, Studia Logica 41 (1982), pp. 41–65.Google Scholar
  22. [RZ]
    Z. W. Ras and M. Zemankova (eds.), Proceedings of the AMC SIGART International Symposium on Methodologies for Intelligent Systems, Knoxville, Tennessee, 1986.Google Scholar
  23. [Sa]
    E. Saarinen, Propositional attitudes are not attitudes towards propositions, in [NS], pp. 130–162.Google Scholar
  24. [Va]
    M. Y. Vardi, On epistemic logic and logical omniscience, in [Ha2], pp. 293–305.Google Scholar
  25. [Wa]
    H. Wansing, Bemerkungen zur Semantik nicht-normaler möglicher Welten, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 35 (1989), pp. 551–557.Google Scholar

Copyright information

© Polish Academy of Sciences 1990

Authors and Affiliations

  • Heinrich Wansing
    • 1
  1. 1.Gruppe für LogikWissenstheorie und Information FU BerlinBerlin 33Germany

Personalised recommendations