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Towards practical implementations of syllogistic

  • Automated Theorem Proving
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EUROCAL '85 (EUROCAL 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 204))

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References

  1. Behmann, H.; "Beiträge zur Algebra der Logik insbesondere zum Entscheidungsproblem". Math. Annalen, 86, pp. 163–220; 1922.

    Article  Google Scholar 

  2. Breban M., Ferro A., Omodeo E. G., Schwartz J. T.; "Decision procedures for elementary sublanguages of Set Theory. II. Formulas involving restricted quantifiers, together with ordinal, integer, map, and domain notions". Comm. Pure App. Math., 34; pp. 177–195; 1981.

    Google Scholar 

  3. Breban M., Ferro A.; "Decision procedures for elementary sublanguages of Set Theory. III. Restricted classes of formulas involving the powerset operator and the general set union operator". To appear in: Advances in Applied Mathematics

    Google Scholar 

  4. Cantone D., Ferro A., Schwartz J.T.; private communications.

    Google Scholar 

  5. Ferro A., Omodeo E. G., Schwartz J. T.; "Decision procedures for elementary sublanguages of Set Theory. I. Multi-level syllogistic and some extensions". Comm. Pure App. Math., 33; pp. 599–608; 1980.

    Google Scholar 

  6. Ferro A., Omodeo E. G., Schwartz J. T.; "Decision procedures for some fragments of Set Theory". Proceedings of the 5th conference on Automated Deduction, pp. 88–96. Springer-Verlag, 1980.

    Google Scholar 

  7. Ferro A., Omodeo E. G.; "An efficient validity test for formulae in extensional two-level syllogistic". Le Matematiche (Catania, Italy), 33; pp. 130–137; 1978.

    Google Scholar 

  8. Gogol, Daniel; "The ∀n∃-completeness of Zermelo-Fraenkel Set Theory". Zeitschr. f. math. Logik und Grundlagen d. Math.; 1978.

    Google Scholar 

  9. Gogol, Daniel; "Sentences with three quantifiers are decidable in Set Theory". Fundamenta Mathematicae CII; 1979.

    Google Scholar 

  10. Lukasiewicz, J.; "Aristotle's syllogistic". Clarendon Press, Oxford; 1952.

    Google Scholar 

  11. Mostowski, A.; Constructible Sets with Applications. North Holland; 1969.

    Google Scholar 

  12. Omodeo E.G.; "Decidability and Proof Procedures for Set Theory with a Choice Operator". Ph. D. Thesis, New York University.

    Google Scholar 

  13. Pastre, Dominique; "Automatic Theorem Proving in Set Theory". Artificial Intelligence, 10; North-Holland; 1978.

    Google Scholar 

  14. Quine, W. V. O.; "Methods of Logic". Henry & Co.; New York; 1959.

    Google Scholar 

  15. Schwartz J. T.; "Instantiation and decision procedures for certain classes of quantified set-theoretic formulae". Inst. for Computer Applications in Science and Engr.; NASA Langley Research Center, Hampton, Viginia, Rept. No. 78-10; 1978.

    Google Scholar 

  16. Shepherdson, J. C.; "On the interpretation of Aristotelian syllogistic". J. Symb. Logic, 21; pp. 137–147; 1956.

    Google Scholar 

  17. Ville, Françoise; "Décidabilité des formules existentielles en théorie des ensembles". C. R. Acad. Sc.; Paris t.272, Serie A, pp.513–516; 1971.

    Google Scholar 

  18. Aho A.V., Hopcroft J.E., Ullman J.D.; The design and analysis of computer algorithms. Addison-Wesley, 1976.

    Google Scholar 

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Bob F. Caviness

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© 1985 Springer-Verlag Berlin Heidelberg

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Ghelfo, S., Omodeo, E.G. (1985). Towards practical implementations of syllogistic. In: Caviness, B.F. (eds) EUROCAL '85. EUROCAL 1985. Lecture Notes in Computer Science, vol 204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15984-3_237

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  • DOI: https://doi.org/10.1007/3-540-15984-3_237

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  • Print ISBN: 978-3-540-15984-1

  • Online ISBN: 978-3-540-39685-7

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