Skip to main content

First order theories of quantification

  • Knowledge Representation
  • Conference paper
  • First Online:
EPIA 89 (EPIA 1989)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 390))

Included in the following conference series:

  • 113 Accesses

Abstract

Many applications of logic to AI require that propositions be reified, i.e., made elements of the domain of discourse. This is needed, in particular, in formalizing reasoning about knowledge and about preconditions of actions. Difficulties arise when the quantificational structure of propositions is essential. We show how ideas from combinatory logic can be used to deal with this problem. This approach allows us to construct first order theories in which lambda-abstraction and quantification can be easily expressed as terms of the language.

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.

Similar content being viewed by others

References

  1. McCarthy, J., “First Order Theories of Individual Concepts and Propositions”, in Hayes, J., Michie, D., and Mikulich, L. (eds.), Machine Intelligence 9. Chichester, UK: Ellis Horwood, 1979, pp. 129–147

    Google Scholar 

  2. Lifschitz, V., Formal theories of action, The Frame Problem, Proc. of the 1987 Workshop (1987) 35–57.

    Google Scholar 

  3. Perlis, D., Languages with Self-Reference I: Foundations, Artificial Intelligence 25 (1985) 301–322.

    Google Scholar 

  4. Kovalski, R., Logic for Problem Solving, New York, NY, North Holland, 1979, p. 136.

    Google Scholar 

  5. Hindley, J. and Seldin, J., Introduction to Combinators and λ-Calculus, Cambridge, Great Britain, University Press, 1986.

    Google Scholar 

  6. Lifschitz, V. and Rabinov, A., Miracles in Formal Theories of Action Artificial Intelligence 38 225–237.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

J. P. Martins E. M. Morgado

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rabinov, A. (1989). First order theories of quantification. In: Martins, J.P., Morgado, E.M. (eds) EPIA 89. EPIA 1989. Lecture Notes in Computer Science, vol 390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51665-4_73

Download citation

  • DOI: https://doi.org/10.1007/3-540-51665-4_73

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51665-1

  • Online ISBN: 978-3-540-46743-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics