Logic of Programs 1985: Logics of Programs pp 406-412 | Cite as

Computer aided reasoning

  • Andrzej Trybulec
  • Howard A. Blair
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 193)


We present a language intended to be a first step in approximating the language of mathematical papers, and a validator; that is, a program that checks the validity of arguments written in this language. The validator approximates the activity of a mathematician in certifying the structure and correctness of the mathematical argument. Both components together constitute a computer aided reasoning (CAR) system. Versions of the system, called MIZAR, have been in use for a decade for discrete mathematics instruction. We are concerned here with the features of the MIZAR language that that are used to diminish the gap between formal natural deduction and mathematical vernacular. The inference checking component of the validator can be easily changed. We demonstrate the influence on the way the expressive power of the language can be exploited by contrasting, for a fixed proposition, two proofs embodying the same idea but for which different checking modules have been used. The more powerful inference checker that we discuss incorporates the formalization of obviousness given by M. Davis.


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  1. [B70]
    Borsuk, Karol, On the homotopy types of some decomposition spaces, Bull.Acad.Pol.Sci., ser.math, astr. et phys. no.5, 18(1970)Google Scholar
  2. [BTZ85]
    Bylinski, Cz., Trybulec, A., Zukowski, S. MIZAR-HPF, Studies in Grammar, Logic, and Rhetorics V, Warsaw University, (to appear).Google Scholar
  3. [dB70]
    de Bruijn, N.G., The mathematical language Automath, its usage and extensions, Lecture Notes in Mathematics, Springer Verlag, 125(1970)Google Scholar
  4. [C82]
    Constable, R.L., An introduction to the PL/CV2 programming logic, Lecture Notes in Computer Science, Springer Verlag, 135(1982)Google Scholar
  5. [D81]
    Davis, Martin, Obvious logical inferences, Proc. of IJCAI-81, Vancouver,BC, August 1981,530–531Google Scholar
  6. [GMW79]
    Gordon, M., Milner, R., Wadsworth, C., Edinburgh LCF, Lecture Notes in Computer Science, Springer Verlag, 78(1980)Google Scholar
  7. [MT85]
    Mostowski, Marcin; Trybulec, Zinaida, A certain experimental computer aided course of logic in Poland, Proc. of World Conference on Computers in Education, Norfolk, VA, July-August 1985, North Holland, (to appear).Google Scholar
  8. [RuDr85]
    Rudnicki, Piotr; Drabent, Wlodzimierz, Proving properties of Pascal programs in Mizar-2, Acta Informatica, Springer Verlag, to appear.Google Scholar
  9. [T84]
    Trybulec, A. On a System of Computer Aided Instruction of Logic, Bulletin of the Section of Logic. Polish Academy of Sciences, Warsaw-Lodz.Google Scholar
  10. [TB85]
    Trybulec, A., & Blair, H. Computer Assisted Reasoning with MIZAR, Proceedings of the Ninth International Joint Conference on Artificial Intelligence, (to appear).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Andrzej Trybulec
    • 1
  • Howard A. Blair
    • 1
  1. 1.EECS U-157 University of ConnecticutStorrs

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