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Hints for the design of a set calculus oriented to Automated Deduction

  • E. G. Omodeo
Part 2: Submitted Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 306)

Keywords

Inference Rule Decision Procedure Choice Operator Automate Deduction Safe Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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6 References

  1. 1.
    Brown F.M.; "Towards the automation of Set Theory and its Logic". Artificial Intelligence, 10 (3), 1978, pp.281–316.Google Scholar
  2. 2.
    Brown F.M.; "An experimental logic based on the fundamental deduction principle". Artificial Intelligence, 30 (2), 1986, pp.117–263.CrossRefGoogle Scholar
  3. 3.
    Pastre Dominique; "Automatic Theorem Proving in Set Theory". Artificial Intelligence, 10; North-Holland; 1978.Google Scholar
  4. 4.
    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
  5. 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. 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. Lecture Notes in Computer Science, 87, Springer-Verlag, 1980.Google Scholar
  7. 7.
    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
  8. 8.
    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". Advances in Applied Mathematics, 5, 1984.Google Scholar
  9. 9.
    Ferro A.; "A note on the decidability of MLS extended by the powerset operator". Comm. Pure App. Math.Google Scholar
  10. 10.
    Cantone D., Ferro A., Micale B., Sorace G.; "Decision procedures for elementary sublanguages of Set Theory. IV. Formulae involving a rank operator or one occurrence of Σ (x)={{y} |y ∈ x}". Comm. Pure App. Math., vol. XL, pp.37–77, 1987.Google Scholar
  11. 11.
    Cantone D., Ferro A., Schwartz J.T.; "Decision procedures for elementary sublanguages of Set Theory. V. Multi-level syllogistic extended by the general union operator". (To appear in: Journal of Computer and System Sciences).Google Scholar
  12. 12.
    Cantone D., Ferro A., Schwartz J.T.; "Decision procedures for elementary sublanguages of Set Theory. VI. Multi-level syllogistic extended by the powerset operator". Comm. Pure App. Math., Special anniversary issue, vol. XXXVIII, pp.549–571, 1985.Google Scholar
  13. 13.
    Omodeo E.G.; "Decidability and Proof Procedures for Set Theory with a Choice Operator". Ph. D. thesis, Courant Institute of Mathematical Sciences, New York University, 1984.Google Scholar
  14. 14.
    Ferro A., Omodeo E.; "Decision procedures for elementary sublanguages of Set Theory. VII. Validity in set theory when a choice operator is present." (To appear in: Comm. Pure and App. Math.)Google Scholar
  15. 15.
    Ghelfo S., Omodeo E.G.; "Towards practical implementations of syllogistic". Eurocal '85, Proceedings Vol.2, pp.40–48, Lecture Notes in Computer Science, 204, 1985.Google Scholar
  16. 16.
    Cantone D., Ferro A., Omodeo E.G.; "Decision procedures for elementary sublanguages of Set Theory. VIII. A semidecision procedure for finite satisfiability of unquantified set-theoretic formulae". (Submitted to: Comm. Pure and App. Math.)Google Scholar
  17. 17.
    Cantone D.A.; "A decision procedure for a class of unquantified formulae of set theory involving the powerset and singleton operators". Ph. D. thesis, Courant Institute of Mathematical Sciences, New York University, January 1987.Google Scholar
  18. 18.
    Cantone D., Ferro A.; "Some recent decidability results in set theory". X incontro di Logica Matematica — La Logica nell'Informatica. Siena, 1986.Google Scholar
  19. 19.
    Cantone D., Ghelfo S., Omodeo E.G.; "The automation of syllogistic. I. Syllogistic normal forms". (Submitted to: Journal of Symbolic Computation), 1986.Google Scholar
  20. 20.
    Cantone D., Ferro A., Omodeo E.G., Schwartz J.T., "Decision algorithms for some fragments of analysis and related areas". (To appear in: Comm. Pure and App. Math.)Google Scholar
  21. 21.
    Parlamento F., Policriti A.; "Decision procedures for elementary sublanguages of Set Theory. X. On the satisfiability of restricted set-theoretic formulas of purely universal form". (Submitted to Comm. Pure and App. Math.), 1986.Google Scholar
  22. 22.
    Parlamento F., Policriti A.; "Decision procedures for elementary sublanguages of Set Theory. IX. Undecidability of set theoretic formulas involving restricted quantifiers". (Submitted to Comm. Pure and App. Math.), 1986.Google Scholar
  23. 23.
    Nelson G.D., Oppen D.; "Simplification by Cooperating Decision Procedures", ACM Transactions on Programming Languages and Systems, Vol.1, No.2, October 1979.Google Scholar
  24. 24.
    Jech T.J.; Set theory, Academic Press; 1978.Google Scholar
  25. 25.
    Hällnas, Lars; "On normalization of proofs in Set theory". Filosofiska istitutionen, Stockholms universitet; 1983.Google Scholar
  26. 26.
    Boyer R., Lusk E., McCune W., Overbeek R., Stickel M., Wos L.; "Set theory in First-Order Logic: Clauses for Gödel's axioms, draft, May 1986.Google Scholar
  27. 27.
    Paige R., Henglein F.; "Mechanical translation of set-theoretic problem specifications into efficient RAM code — a case study". Eurocal '85, Proceedings Vol.2, pp.554–567, Lecture Notes in Computer Science, 204, 1985.Google Scholar
  28. 28.
    Paige R.; Formal Differentiation. UMI Research Press, Ann Arbor, Mich., 1981. Revision of Ph.D. thesis, NYU, June 1979.Google Scholar
  29. 29.
    Paige R., "Programming with invariants". IEEE Software, Jan 1986, pp.56–69.Google Scholar
  30. 30.
    Beeson M.; "Normalization of Terms in Logic and Computer Science". Presented at the Conference on Logic and Computer Science: New Trends and Applications, Turin, Italy, 1986.Google Scholar
  31. 31.
    Beeson M.; "Towards a Computation System Based on Set Theory". 1986.Google Scholar
  32. 32.
    Martin-Löf P.; Intuitionistic Type Theory, Bibliopolis, Napoli, Italy, 1984.Google Scholar
  33. 33.
    Coquand T., Huet G.; "Constructions: A higher order proof system for mechanizing mathematics". In: Buchberger B. (ed.); EUROCAL '85: European Conference on Computer Algebra, Lecture Notes in Computer Science 203, pp.151–184, Springer-Verlag, Berlin/Heidelberg/New York, 1985.Google Scholar
  34. 34.
    de Brujin N.G.; "A survey of the project AUTOMATH", In: Seldin J.P. and Hindley J.R. (eds.), To H.B. Curry: Essays on Combinator Logic, Lambda Calculus and Formalism, Academic Press, New York, 1980.Google Scholar
  35. 35.
    Constable R., et al.; Implementing Mathematics with the Nuprl Proof development System. Prentice-Hall, Englewood Cliffs, New Jersey, 1986.Google Scholar
  36. 36.
    Schwartz J.T., Dewar R.B.K., Dubinsky E., Schonberg E.; Programming with sets. An Introduction to Setl. Lecture Notes in Computer Science (Springer Verlag), 1986.Google Scholar
  37. 37.
    McCarthy, J.; private communication to Martin Davis, 1977.Google Scholar
  38. 38.
    Perlis, D.; "Commonsense Set Theory", 1986.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • E. G. Omodeo
    • 1
  1. 1.ENIDATA-SOPEBBolognaItaly

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