Abstract
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).
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
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.
J. F. A. K. van Benthem, Correspondence theory, in [GG], vol. II, 1984, pp. 167–247.
R. Carnap, Meaning and Necessity, Chicago University Press, 1947.
B. F. Chellas, Modal Logic: An Introduction, Cambridge University Press, 1980.
M. J. Cresswell, Intensional logics and logical truth, Journal of Philosophical Logic 1 (1972), pp. 2–15.
M. J. Cresswell, Hyperintensional logic, Studia Logica 34 (1975), pp. 25–38.
J. M. Dunn, Relevance logic and entailment, in [GG], vol. III, 1986, pp. 117–224.
R. Fagin and J. Y. Halpern, Belief, awareness, and limited reasoning, Artificial Intelligence 34 (1988), pp. 39–76.
D. Gabbay and F. Guentner (eds.), Handbook of Philosophical Logic, vols. I–IV, Reidel, Dordrecht, 1984–1989.
J. Y. Halpern, Reasoning about knowledge: An overview, in [Ha2], pp. 1–17.
J. Y. Halpern (ed.), Theoretical Aspects of Reasoning about Knowledge: Proceedings of the 1986 Conference, Morgan Kaufmann, Los Altos, 1986.
J. Hintikka, Knowledge and Belief: An Introduction to the Logic of the Two Notions, Cornell University Press, 1962.
J. Hintikka, Impossible possible worlds vindicated, Journal of Philosophical Logic 4 (1975), pp. 475–484.
W. van der Hoek and J.-J Ch. Meyer, Possible logics for belief, Rapport IR-170, Vrije Universiteit Amsterdam, 1988.
K. Konolige, What awareness isn't: A sentential view of implicit and explicit belief, in [Ha2], pp. 241–250.
H. J. Levesque, A logic of implicit and explicit belief, Proceedings AAAI-84, Austin, Texas, 1984, pp. 198–202.
I. Niiniluoto and E. Saarinen (eds.), Intensional Logic: Theory and Applications (Acta Philosophica Fennica 35), Helsinki, 1982.
R. Parikh, Knowledge and the problem of logical omniscience, in [RZ], pp. 432–439.
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.
V. Rantala, Impossible worlds semantics and logical omniscience, in [NS], pp. 106–115.
V. Rantala, Quantified modal logic: Non-normal worlds and propositional attitudes, Studia Logica 41 (1982), pp. 41–65.
Z. W. Ras and M. Zemankova (eds.), Proceedings of the AMC SIGART International Symposium on Methodologies for Intelligent Systems, Knoxville, Tennessee, 1986.
E. Saarinen, Propositional attitudes are not attitudes towards propositions, in [NS], pp. 130–162.
M. Y. Vardi, On epistemic logic and logical omniscience, in [Ha2], pp. 293–305.
H. Wansing, Bemerkungen zur Semantik nicht-normaler möglicher Welten, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 35 (1989), pp. 551–557.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wansing, H. A general possible worlds framework for reasoning about knowledge and belief. Studia Logica 49, 523–539 (1990). https://doi.org/10.1007/BF00370163
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00370163