Skip to main content

A posteriori knowledge: from ambiguous knowledge and undefined information to knowledge

  • Conference paper
  • First Online:
Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU 1995)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 946))

Abstract

Adequate treatment of incomplete and ambiguous information encourage research in theories about reasoning and action (e. g. [7]). In [10] is proposed to deal with this topic using Belnap's four-valued logic. In this paper, Driankov's semantic is used in a formalisation that captures the dynamic character of knowledge and belief. Ambiguous knowledge is present in several kind of situations that formally corresponds with knowing that a disjunction is true, but it is not known which element of the disjunction makes it true. We define an a posteriori knowledge operator that allows to extend knowledge from ambiguous knowledge or undefined information, being in the meanwhile, potential knowledge. In addition, belief is consider local knowledge.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alvarado, M.: Relatives Knowledge and Belief in SKL ** Preferred Model Frames In Proc. of AIMSA94 (Sofia, Bulgaria, 1994)

    Google Scholar 

  2. Alvarado, M.: A posteriori Knowledge: from Ambiguous Knowledge and Undefined Information to Knowledge. Report de Recerca LSI-94-. (UPC, Spain 1994)

    Google Scholar 

  3. Belnap, N.: A Useful Four-Valued Logic. In Modern Use of Logic. (Reidel Publishing Co., 1976)

    Google Scholar 

  4. Van Benthem, J.: A Manual of Intensional Logic CSLI 1 (Stanford, 1988)

    Google Scholar 

  5. Blamey, S.: Partial Logic In Handbook of Philosophical Logic, III. D. Gabbay, F. Guenthner, (Eds.) (Reidel Publishing Co, 1986).

    Google Scholar 

  6. Brewka, G.: Preferred Subtheories: an Extended Logical Framework for Default Reasoning. In Proc. IJCAI89. (Detroit, USA, 1989).

    Google Scholar 

  7. Brewka, G., Hertzberg, J.: How to do things with worlds: On formalizing revision and reasoning about action. In Journal of Logic and Computation. (1993)

    Google Scholar 

  8. Del Val, A., Shoham, Y.: Deriving Properties of Belief Update from Theories of Action (II). In Proc. IJCAI'93

    Google Scholar 

  9. Doherty, P.: NMR-3 A Three-Valued Approach to Non-Monotonic Reasoning. PhD Theses (Linköping, 1992).

    Google Scholar 

  10. Driankov, D.: Computing Effects of Ambiguous Actions in Incomplete Worlds: The Epistemic State Approach. Linköping University (Sweden, 1994)

    Google Scholar 

  11. Gärdenfors, P.: Knowledge in Flux The MIT Press (1988).

    Google Scholar 

  12. J. Halpern, Moses, Y.: A Guide to Completeness and Complexity for Modal Logics of Knowledge and Belief. Artificial Intelligence 54 (1992) pp. 319–379.

    Article  Google Scholar 

  13. Hintikka, J.: Knowledge and Belief (Cornell University Press 1962).

    Google Scholar 

  14. Kleene, S.: Introduction to Metamathematical (North Holland, Amsterdam, 1952).

    Google Scholar 

  15. Kripke, S.: A completness theorem in modal logic. The Journal of Symbolic Logic. 24-1 (1959) pp. 1–14.

    Google Scholar 

  16. Levesque, H.: A Logic of Implicit and Explicit Belief. Proceedings of the AAAI (1984).

    Google Scholar 

  17. McCArthy, J.: Circumscription — A Form of Nonmonotonic Reasoning. Artificial Intelligence (1986).

    Google Scholar 

  18. Meyer, J., Van der Hoek, W.: A Cumulative Default Logic Based on Epistemic States. Rapportnr. IR-288. August 1992. Vrije Universitet, Amsterdam

    Google Scholar 

  19. Núñez, G., Alvarado, M.: Hacia una semántica realista de mundos posibles en lógica de creencias. Reporte de Investigación LANIA (México, 1993).

    Google Scholar 

  20. Sandewall, E.: The Semantics of Non-Monotonic Entailment Defined Using Partial Interpretations. LiTH-IDA-R-88-31, Linköping University (Sweden, 1988)

    Google Scholar 

  21. Shoham, Y.: Reasoning About Change (The MIT Press, 1988).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Christine Froidevaux Jürg Kohlas

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Alvarado, M. (1995). A posteriori knowledge: from ambiguous knowledge and undefined information to knowledge. In: Froidevaux, C., Kohlas, J. (eds) Symbolic and Quantitative Approaches to Reasoning and Uncertainty. ECSQARU 1995. Lecture Notes in Computer Science, vol 946. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60112-0_2

Download citation

  • DOI: https://doi.org/10.1007/3-540-60112-0_2

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60112-8

  • Online ISBN: 978-3-540-49438-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics