Reasoning with the unknown

  • Nuno J. Mamede
  • Carlos Pinto-Ferreira
  • João P. Martins
Automated Deduction
Part of the Lecture Notes in Computer Science book series (LNCS, volume 390)


We define a logical system with four values, the traditional truth values T and F and two “Unknown” values. An inference system based on this logic has the capability to remember all the paths followed during an attempt to answer a question. For each path it records the used hypotheses (the hypotheses that constitute the path), the missing hypothesis (when the path did not lead to an answer), and why it was assumed as missing. The inference system takes special care with missing hypotheses that are contradictory with any hypothesis that is being considered. An inference system with these capabilities can report the answers found and the reasons that prevented the inference of other potential answers. This capability can be used to plan reasoning, to perform default reasoning, and to reason about its own knowledge.


Inference System Inference Rule Propositional Logic Belief Revision Conditional Support 
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. Ackermann R., An Introduction to Many-valued Logics, New York: Dover Publications Inc., 1967.Google Scholar
  2. Belnap N., “A Useful Four-valued Logic”, in Modern Uses of Multi-valued Logic, G. Epstein and M. Dunn (ed.), Dordrecht: Reidel, 1977.Google Scholar
  3. Bochvar D., “On Three-valued Logical Calculus and its Application to the Analysis of Contradictions", Matematiceskij Sbornik 4, pp. 353–369, 1939.Google Scholar
  4. Golshani F., “Growing Certainty with Null Values”, Information Systems 10, No. 3, pp. 289–297, 1985.Google Scholar
  5. Haack S., Philosophy of Logics, Cambridge, UK: Cambridge University Press, 1978.Google Scholar
  6. Kleene S., Introduction to Metamathematics, New York: Van Nostrand, 1952.Google Scholar
  7. Lukasiewicz J., “Many-Valued Systems of Propositional Logic”, in McCall (ed.), Polish Logic: 1920–1939, Oxford, pp. 16–18, 1930.Google Scholar
  8. Mamede N. and Martins J., “Reasoning with the Unknown”, GIA Technical Report 89/3, Instituto Superior Técnico, Technical University of Lisbon, 1989.Google Scholar
  9. Martins J., Reasoning in Multiple Belief Spaces, Ph.D. Dissertation, Technical Report 203, Department of Computer Science, SUNY at Buffalo, 1983.Google Scholar
  10. Martins J. and Shapiro S., “A Model for Belief Revision”, Proceedings Non-Monotonic Reasoning Workshop, Menlo Park, CA: AAAI, pp. 241–294, 1984.Google Scholar
  11. Martins J. and Shapiro S., “A Model for Belief Revision”, Artificial Intelligence 35, No. 1, pp. 25–79, 1988.Google Scholar
  12. McKay D., “Monitors: Structuring Control Information”, Thesis proposal, Department of Computer Science, SUNY at Buffalo, 1981.Google Scholar
  13. Rescher N., “Quasi-Truth-Functional Systems of Propositional Logic”, The Journal of Symbolic Logic, 27, No. 1, pp. 1–10, 1962.Google Scholar
  14. Rescher N., Many-valued Logic, McGraw-Hill, 1969.Google Scholar
  15. Shapiro S., personal communication, 1989Google Scholar
  16. Turner R., Logics for Artificial Intelligence, Chichester, UK: John Wiley & Sons, 1984.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Nuno J. Mamede
    • 1
  • Carlos Pinto-Ferreira
    • 1
  • João P. Martins
    • 1
  1. 1.Instituto Superior TécnicoTechnical University of LisbonLisboaPortugal

Personalised recommendations