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Decision procedures for elementary sublanguages of set theory. I: Multi- level syllogistic and some extensions. (English) Zbl 0453.03009


MSC:

03B25 Decidability of theories and sets of sentences
03E99 Set theory
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[1] Behmann, Math. Annalen 86 pp 163– (1922)
[2] Davis, J. Appl. Comput. Math. 7 pp 201– (1960)
[3] Aristotle’s Syllogistic, Clarendon Press, Oxford, 1952.
[4] and , A simplifier based on efficient decision algorithms, Fifth Ann. Symp. on Principles of Programming Languages, 1978, pp. 141–150.
[5] Complexity of combinations of quantifier-free procedures, Workshop on Automatic Deduction, Austin, Texas, 1979.
[6] On specifying verifiers, Proc. of Conf. on Principles of Programming Languages, ACM, New York City, 1979, pp. 106–116.
[7] Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt, Comptes-rendus du premiere Congres des Mathematicien des Pays Slaves, Warsaw, 1930, pp. 92–101. · JFM 56.0825.04
[8] Methods of Logic, Henry Holt, New York, 1950.
[9] Instantiation and decision procedures for certain classes of quantified set-theoretic formulae, Inst. for Computer Appl. in Science and Engineering, NASA Langley Research Center, Hampton, VA, Report #7810, 1978.
[10] A survey of program proof technology, Courant Institute, Computer Science Dept., Report #1, September 1978.
[11] Shepherdson, J. Symbolic Log. 21 pp 137– (1956)
[12] Ordinal Algebras, North Holland, New York, 1956.
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