Skip to main content
SpringerLink
Log in
SpringerLink
Log in

Explicit and Implicit Beliefs

  • Conference paper
GWAI-86 und 2. Österreichische Artificial-Intelligence-Tagung

Part of the book series: Informatik-Fachberichte ((2252,volume 124))

Abstract

We provide an answer to the three questions asked by H.J.Levesque during his AAAI-84 presentation:

  1. 1.

    How to distinguish between local and global inconsistencies i.e. between Believe(p) & Believe(¬p) and Belicve(p&¬p) ?

  2. 2.

    How to introduce quantifiers to the logic of beliefs ?

  3. 3.

    Is it possible to determine whether an agent explicitly believes in a statement p in a time better then O(KB*p) ?

We introduce a logic of explicit and implicit beliefs B#L, which allows local inconsistencies, but forbids global ones. We prove its soundness and completeness. The semantics for the B#L logic is given by a Kripke model. We show how to introduce quantifiers to this logic and discuss its computational properties.

The paper is organized as follows

  1. 1.

    Introduction.

  2. 2.

    The logics of explicit beliefs.

  3. 3.

    Implication in E fde , and E x .

  4. 4.

    Implicit and Explicit Beliefs.

  5. 5.

    The semantics of beliefs.

  6. 6.

    Tractability of implication.

  7. 7.

    Final remarks.

  8. 8.

    References.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H.J. Levesque, A Logic of Implicit and Explicit Beliefs, AAAI 1984.

    Google Scholar 

  2. A.R. Anderson, N.D. Belnap, Entaiment, The Logic of Relevance and Necessity, Princeton University Press 1975.

    Google Scholar 

  3. N.D. Belnap, A Useful Four Valued Logic, in: G. Epstein, J.M. Dunn (eds.) Modern Uses of Multiple Valued Logic, Reidel, 1977.

    Google Scholar 

  4. A.R. Anderson, N.D. Belnap, First Degree Entailments, Math. Annalen 149, 1963.

    Google Scholar 

  5. A.R. Anderson,Completeness Theorems for the System E of Entailment and EQ of Entailment with Quantification,Zeitschr. f. math. Logik u. Grunglagen d. Math. Bd.6, 1960.

    Google Scholar 

  6. P. Hajek, T. Havranek, Mechanizing Hypothesis Formation, Springer 1978.

    Google Scholar 

  7. J.Y. Halpern, R. Fagin, Belief, Awereness, and Limited Reasoning: Preliminary Report, IJCAI -1985.

    Google Scholar 

  8. R.C. Lyndon, Notes on Logic, D. van Nostrand Company, Inc. 1966.

    Google Scholar 

  9. P.S. Patel-Schneider, A Decidable First Order Logic for Knowledge Representation, IJCAI -1985.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IBM T.J.Watson Research Center, P.O. Box 218, Yorktown Heights, NY, 10598, UK

    Włodzimierz Zadroƶny

Authors
  1. Włodzimierz Zadroƶny
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. IBM Deutschland GmbH, Abt. LILOG 3504, Postfach 800880, D-7000, Stuttgart 80, Germany

    Claus-Rainer Rollinger

  2. Institut für Medizinische Kybernetik und Artificial Intelligence, Universität Wien, Freyung 6, A-1010, Wien, Austria

    Werner Horn

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zadroƶny, W. (1986). Explicit and Implicit Beliefs. In: Rollinger, CR., Horn, W. (eds) GWAI-86 und 2. Österreichische Artificial-Intelligence-Tagung. Informatik-Fachberichte, vol 124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71385-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-71385-9_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16808-9

  • Online ISBN: 978-3-642-71385-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation