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On the complexity of propositional quantification in intuitionistic logic

Published online by Cambridge University Press:  12 March 2014

Philip Kremer
Philip Kremer*
Affiliation:
Department of Philosophy, Yale University, P.O. Box 208306, New Haven, CT 06520-8306, USA, E-mail: [email protected]
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Abstract

We define a propositionally quantified intuitionistic logic Hπ+ by a natural extension of Kripke's semantics for propositional intuitionistic logic. We then show that Hπ+ is recursively isomorphic to full second order classical logic. Hπ+ is the intuitionistic analogue of the modal systems S5π+, S4π+, S4.2π+, K4π+, Tπ+, Kπ+ and Bπ+, studied by Fine.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 2 , June 1997 , pp. 529 - 544
Copyright
Copyright © Association for Symbolic Logic 1997

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References

REFERENCES

[1970] Fine, K., Propositional quantifiers in modal logic, Theoria, pp. 336–346.Google Scholar
[1974] Gabbay, D., On 2nd order intuitionistic propositional calculus with full comprehension, Archiv für Mathematische Logik und Grundlagenforsch, pp. 177–186.Google Scholar
[1981] Gabbay, D., Semantical investigations in Heyting's intuitionistic logic, D. Reidel, Dordrecht.CrossRefGoogle Scholar
[1950] Henkin, L., Completeness in the theory of types, this Journal, pp. 81–91.Google Scholar
[1970] Kaplan, D., S5 with quantifiable propositional variables, this Journal, p. 355.Google Scholar
[1981] Kreisel, G., Monadic operators defined by means of propositional quantification in intuitionistic logic, Reports on Mathematical Logic, pp. 9–15.Google Scholar
[1993] Kremer, P., Quantifying over propositions in relevance logic: Non-axiomatisability of ∀p and ∃p, this Journal, pp. 334–349.Google Scholar
[1963] Kripke, S., Semantical analysis of intuitionistic logic I, Formal systems and recursive functions: Proceedings of the eighth logic colloquium (Crossley, J. N. and Dummett, M. A. E., editors), North-Holland, Amsterdam, pp. 92–130.Google Scholar
[1976] Löb, M. H., Embedding first order predicate logic in fragments of intuitionistic logic, this Journal, pp. 705–718.Google Scholar
[1980] Nerode, A. and Shore, R., Second order logic and first order theories of reducibility orderings, The Kleene symposium (Barwise, J., Keisler, H. J., and Kunen, K., editors), North-Holland, Amsterdam, pp. 181–200.CrossRefGoogle Scholar
[1992] Pitts, A. M., On an interpretation of second order quantification in first order intuitionistic propositional logic, this Journal, pp. 33–52.Google Scholar
[1965] Rabin, M., A simple method for undecidability proofs and some applications, Logic, methodology and the philosophy of science, proceeding of the 1964 international congress (Bar-Hillel, Y., editor), North-Holland, Amsterdam, pp. 58–68.Google Scholar
[1984] Scedrov, A., On some extensions of second-order intuitionistic propositional calculus, Annals of Pure and Applied Logic, pp. 155–164.Google Scholar
[1977] Sobolev, S. K., On the intuitionistic propositional calculus with quantifiers (in Russian), Akademiya Nauk Soyuza SSR. Matematicheskie Zamietki, pp. 69–76.Google Scholar