Skip to main content
Log in

“Conservative” Kripke closures

  • Published:
Synthese Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Barnes, R. F. and R. D. Gumb: 1979, ‘The Completeness of Presupposition Free Tense Logic’, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik (hereafter ZMLGM) 25, 193–208.

    Google Scholar 

  2. Boolos, G.: 1979 The Unprovability of Consistency. Cambridge: Cambridge University Press.

    Google Scholar 

  3. Fine, K.: 1979 ‘Failures of the Interpolation Lemma in Quantified Modal Logic’, Journal of Symbolic Logic, 44 201–206.

    Google Scholar 

  4. Fine, K.: 1978, ‘Model Theory for Modal Logic, Part I-The De Re/De Dicto Distinction’, Journal of Philosophical Logic, 7 125–156.

    Google Scholar 

  5. Gabbay, D.: 1975 ‘Modal Theory for Tense Logics’, Annals of Mathematical Logic 8, 185–236.

    Google Scholar 

  6. Gumb, R. D., ‘Comments on Probabilistic Semantics’, [15]

    Google Scholar 

  7. Gumb, R. D. ‘The Craig-Lyndon Interpolation Lemma for (Free) Intuitionistic Logic with Equality’, [15]

    Google Scholar 

  8. Gumb, R. D.: 1979, Evolving Theories. New York: Haven, 1979.

    Google Scholar 

  9. Gumb, R. D.: 1984, ‘An Extended Joint Consistency Theorem for a Family of Free Modal Logics with Equality’, Journal of Symbolic Logic, 49.

  10. Gumb, R. D.: 1972, Rule-Governed Linguistic Behavior, Mouton, The Hague.

    Google Scholar 

  11. Gumb, R. D. ‘A Translation of (Free) Intuitionistic Logic with Equality into Free S4 with Equality and Increasing Domains’, [15]

    Google Scholar 

  12. Harper, W. L.: ‘A Conditional Belief Semantics for Free Quantificational Logic with Identity’, in [15]

    Google Scholar 

  13. Leblanc, H.: 1976, Truth-Value Semantics North Holland, Amsterdam.

    Google Scholar 

  14. Leblanc, H. and Gumb, R. D.: ‘Completeness and Soundness Proofs for Three Brands of Intuitionistic Logic’, in [15]

    Google Scholar 

  15. Leblanc, H., Gumb, R. D., and Stern, R. (eds.): 1983, Essays in Semantics and Epistemology, Haven, New York.

    Google Scholar 

  16. Lemmon, E. J.: 1977, An Introduction to Modal Logic, Basil Blackwell, Oxford.

    Google Scholar 

  17. Makinson, D. C.: 1966, ‘On Some Completeness Theorems in Modal Logic’ ZMLGM 12 379–384.

    Google Scholar 

  18. Sahlqvist, H.: 1975, ‘Completeness and Correspondence in the First and Second Order Semantics for Modal Logic’ in S. Kanger (ed.), Proceedings of the Third Scandinavian Logic Symposium, Uppsala 1973, North Holland, Amsterdam.

    Google Scholar 

  19. Weaver, G. and R. D. Gumb' 1982, ‘First Order Properties of Relations with the Monotonic Closure Property’, ZMLGM, 28, 1–5.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This paper summarizes work performed under a 1978–80 grant from the Foundation for the Advancement of Interdisciplinary Studies for research on evolving theories, intensional logics, probabilistic semantics, and applications of them to the semantics of natural languages. I have been interested in applications of logic to the semantics of natural languages for some time [10, p. 104]; needless to say, applications of the systems discussed in this paper stand in need for further articulation. I would like to express my appreciation to my friends Bob Barnes, Hugues Leblanc, and George Weaver for having worked with me over the past few years.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gumb, R.D. “Conservative” Kripke closures. Synthese 60, 39–49 (1984). https://doi.org/10.1007/BF00485617

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00485617

Navigation