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Automatic theorem proving in set theory. (English) Zbl 0374.68059


MSC:

68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
03Exx Set theory
03-04 Software, source code, etc. for problems pertaining to mathematical logic and foundations
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Full Text: DOI

References:

[1] (Abadie, J., Integer and Nonlinear Programming (1970), American Elsevier: American Elsevier New York) · Zbl 0321.00011
[2] Brown, F. M., Doing arithmetic without diagrams, Artificial Intelligence, 8, 179-200 (1977) · Zbl 0359.68108
[3] Brown, F. M., Towards the automation of set theory and its logic, Submitted to Artificial Intelligence; Brown, F. M., Towards the automation of set theory and its logic, Submitted to Artificial Intelligence · Zbl 0395.68082
[4] Halmos, P. R., Notice Set Theory (1960), Van Nostrand: Van Nostrand Princeton · Zbl 0117.10502
[5] Barachen, L.; Wos, L., Unit refutations and born sets, J. ACM, 21, 590-605 (1974) · Zbl 0296.68093
[6] Brivise, J. L., Theorie Axiomatique des Ensembles (1969), P.U.F.: P.U.F. Paris · Zbl 0175.00601
[7] Newma, A. J., A relaxation approach to splitting in an automatic theorem prover, Artificial Intelligence, 6, 25-39 (1975) · Zbl 0301.68087
[8] Nevis, A. J., Plane geometry theorem proving using forward chaining, Artificial Intelligence, 6, 1-23 (1975) · Zbl 0301.68086
[9] Petersen, G. E., Theorem proving with lemmas, J. ACM, 23, 573-581 (1976) · Zbl 0333.68061
[10] Sigler, L. E., Exercises in Set Theory (1966), Van Nostrand: Van Nostrand London · Zbl 0144.24803
[11] Slogle, J. E., Automatic theorem proving with built-in theories including equality, partial ordering and sets, J. ACM, 19, 120-135 (1972) · Zbl 0231.68035
[12] Slagla, J. R.; Norton, J. M., Experiments with an automatic theorem-prover having partial ordering inference rules, C. ACM, 16, 682-688 (1973) · Zbl 0271.68062
[13] Slagla, J. R.; Norton, J. M., Automated theorem proving for the theories of partial and total ordering, Computer Journal, 18, 49-54 (1973) · Zbl 0296.68091
[14] Wang, H., Towards mechanical mathematics, IBM Journal of Research and Development, 4, 2-22 (1960)
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