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Procedure implementation through demodulation and related tricks

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Book cover 6th Conference on Automated Deduction (CADE 1982)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 138))

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Abstract

In writing a computer program, the programmer often uses procedures or subroutines to carry out frequently-occurring subsidiary tasks. These tasks range from simple bookkeeping and updating to the seeking of the generalization of two given formulas. Problems that one wishes to solve with the assistance of an automated theorem-proving program likewise often involve subsidiary tasks and the corresponding need for procedures (or their equivalent) to accomplish them. It is reasonable to conjecture that employment of procedures either requires the use of external programs or requires substantial modification of the existing theorem-proving program itself. In this paper we give examples that show that neither is the case. Demodulation is the key to implementing the procedures that accomplish such frequently-occurring tasks.

We give here sets of demodulators for accomplishing a wide variety of tasks. The most complex given demodulator set enables the program to find the least general subsumer of two given unit clauses. We also consider questions of counting and classifying, bookkeeping and updating, and cleanup after case analysis. Finally, we give a set of demodulators for coping with set-theory in an efficient and natural way.

The material presented here is but a sample of the additional possibilities for the use of demodulation. Since it was not known how to accomplish some of the cited tasks purely within the context of automated theorem proving, the examples given here may lead to an expanded use of automated theorem-proving programs in general. Thus, although the use of demodulation for both simplification and canonicalization demonstrates its value, it turns out that demodulation is even more powerful than was realized.

This work was supported in part by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under Contract W-31-109-Eng-38 (Argonne National Laboratory, Argonne, IL 60439) and in part by NSF grant MCS79-03870 (Northern Illinois University, DeKalb, IL 60115).

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Authors and Affiliations

  1. Argonne National Laboratory, 60439, Argonne, Illinois

    S. K. Winker & L. Wos

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  1. S. K. Winker
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  2. L. Wos
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D. W. Loveland

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© 1982 Springer-Verlag Berlin Heidelberg

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Winker, S.K., Wos, L. (1982). Procedure implementation through demodulation and related tricks. In: Loveland, D.W. (eds) 6th Conference on Automated Deduction. CADE 1982. Lecture Notes in Computer Science, vol 138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0000054

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  • DOI: https://doi.org/10.1007/BFb0000054

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  • Print ISBN: 978-3-540-11558-8

  • Online ISBN: 978-3-540-39240-8

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