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Decision procedures for elementary sublanguages of set theory: XI. Multilevel syllogistic extended by some elementary map constructs

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Abstract

This paper gives a decision procedure for the class of set-theoretic formulae in the unquantified language ℒ involving Boolean set operators, set equality and membership, domain and range operators, direct and inverse image operators, as well as the predicates SINGLEVALUED, INJECTIVE, and INV (for inverse).

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References

  1. Cantone, D., ‘Decision procedures for elementary sublanguages of set theory. X. Multilevel syllogistic extended by the singleton and powerset operators’, J. Automated Reasoning 7, 193–230.

  2. CantoneD., FerroA., SchwartzJ. T., ‘Decision procedures for elementary sublanguages of set theory. V. Multi-level syllogistic extended by the general union operator’, J. Comp. Syst. Sci. 34, 1–18 (1987).

    Google Scholar 

  3. CantoneD., GhelfoS., and OmodeoE. G., ‘The automation of syllogistic. I. Syllogistic normal forms’, J. Symb. Comp. 6, 83–98 (1988).

    Google Scholar 

  4. Ferro, A., Omodeo, E. G., and Schwartz, J. T., ‘Decision procedures for some fragments of set theory’, 5th Conference on Automated Deduction, Les Arcs, France (Bibel, W. and Kowalski, R., eds.). Springer Lecture Notes on Computer Science 87, 88–96 (1980).

  5. JechT., Set Theory, Academic Press, New York, 1978.

    Google Scholar 

  6. Parlamento, F. and Policriti, A., ‘On the representability of well-founded graphs and the axiom of choice’, Manuscript, 1988.

  7. Schwartz, J. T., Dewar, R. K. B. Dubinsky, E., and Schonberg, E., Programming with sets. Text and Monographs in Computer Science, Springer-Verlag, 1986.

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Authors and Affiliations

  1. Dipartimento di Matematica Pura e Applicata, Università degli Studi di L'Aquila, Italy

    D. Cantone

  2. Computer Science Department, Courant Institute of Mathematical Sciences, 10012, New York, New York, U.S.A.

    J. T. Schwartz

Authors
  1. D. Cantone
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  2. J. T. Schwartz
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Additional information

This paper was written while the first author was a Visiting Professor at Courant Institute, New York University, U.S.A.

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Cantone, D., Schwartz, J.T. Decision procedures for elementary sublanguages of set theory: XI. Multilevel syllogistic extended by some elementary map constructs. J Autom Reasoning 7, 231–256 (1991). https://doi.org/10.1007/BF00243808

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  • DOI: https://doi.org/10.1007/BF00243808

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