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On simplifying the matrix of a wff

Published online by Cambridge University Press:  12 March 2014

Peter Andrews
Peter Andrews*
Affiliation:
Carnegie-Mellon University
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Extract

In [3], [4], and [5] Joyce Friedman formulated and investigated certain rules which constitute a semi-decision procedure for wffs of first order predicate calculus in closed prenex normal form with prefixes of the form ∀x1 … ∀xκ∃y1 … ∃ym∀z1 … ∀zn. Given such a wff QM, where Q is the prefix and M is the matrix in conjunctive normal form, Friedman's rules can be used, in effect, to construct a matrix M* which is obtained from M by deleting certain conjuncts of M.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 33 , Issue 2 , 23 July 1968 , pp. 180 - 192
Copyright
Copyright © Association for Symbolic Logic 1968

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References

[1]Church, Alonzo, A formulation of the simple theory of types, this Journal, vol. 5 (1940), pp. 56–68.Google Scholar
[2]Church, Alonzo, Introduction to mathematical logic, vol. I, Princeton University Press, Princeton, N.J., 1956.Google Scholar
[3]Friedman, Joyce, A semi-decision procedure for the functional calculus, Journal of the Association for Computing Machinery, vol. 10 (1963), pp. 1–24.CrossRefGoogle Scholar
[4]Friedman, Joyce, A computer program for a solvable case of the decision problem, Journal of the Association for Computing Machinery, vol. 10 (1963), pp. 348–356.CrossRefGoogle Scholar
[5]Friedman, Joyce, A new decision procedure in logic with a computer realization, Ph.D. thesis, Harvard University, 1964.Google Scholar
[6]Henkin, Leon, Completeness in the theory of types, this Journal, vol. 15 (1950), pp. 81–91.Google Scholar
[7]Quine, W. V., A proof procedure for quantification theory, this Journal, vol. 20 (1955), pp. 141–149.Google Scholar
[8]Robinson, J. A., A machine-oriented logic based on the resolution principle, Journal of the Association for Computing Machinery, vol. 12 (1965), pp. 23–41.CrossRefGoogle Scholar
[9]Wang, Hao, Logic of many-sorted theories, this Journal, vol. 17 (1952), pp. 105–116.Google Scholar