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A reduction class containing formulas with one monadic predicate and one binary function symbol

Published online by Cambridge University Press:  12 March 2014

Charles E. Hughes
Charles E. Hughes*
Affiliation:
University of Tennessee, Knoxville, Tennessee 37916
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Abstract

A new reduction class is presented for the satisfiability problem for well-formed formulas of the first-order predicate calculus. The members of this class are closed prenex formulas of the form ∀x∀yC. The matrix C is in conjunctive normal form and has no disjuncts with more than three literals, in fact all but one conjunct is unary. Furthermore C contains but one predicate symbol, that being unary, and one function symbol which symbol is binary.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 41 , Issue 1 , March 1976 , pp. 45 - 49
Copyright
Copyright © Association for Symbolic Logic 1976

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References

REFERENCES

[1] Börger, E., Reduction classes of Krom formulae with only one predicate symbol and function symbols, Notices of the American Mathematical Society, vol. 20 (1973), A–286. Abstract.Google Scholar
[2] Church, A., Introduction to mathematical logic, Vol. I, Princeton University Press, Princeton, N.J., 1956.Google Scholar
[3] Davis, M., Computability and unsolvability, McGraw-Hill, New York, 1958.Google Scholar
[4] Hughes, C. E., Two variable implicational calculi of prescribed many-one degrees of unsolvability, this Journal, vol. 41 (1976), pp. 39–45.Google Scholar
[5] Krom, M. R., The decision problem for formulas in prenex conjunctive normal form with binary disjunction, this Journal, vol. 35 (1970), pp. 210–216.Google Scholar