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Interpretations of intuitionist logic in non-normal modal logics

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Abstract

Historically, it was the interpretations of intuitionist logic in the modal logic S4 that inspired the standard Kripke semantics for intuitionist logic. The inspiration of this paper is the interpretation of intuitionist logic in the non-normal modal logic S3: an S3 model structure can be 'looked at' as an intuitionist model structure and the semantics for S3 can be 'cashed in' to obtain a non-normal semantics for intuitionist propositional logic. This non-normal semantics is then extended to intuitionist quantificational logic.

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REFERENCES

  1. Brouwer, L. E. J., 'Consciousness, Philosophy, and Mathematics', in Collected Works I, ed. A. Heyting, pp. 480–494 (North-Holland, Amsterdam, 1975).

    Google Scholar 

  2. Gödel, K., 'An interpretation of the intuitionistic propositional calculus', in Collected Works, vol. 1, eds. S. Feferman et al., pp. 301, 303 (Oxford University press, New York, 1986).

    Google Scholar 

  3. Grzegorczyk, A., 'Some relational systems and the associated topological spaces', Fundamenta Mathematicae 60 1964, 223–231.

    Google Scholar 

  4. Hacking, I., 'What is Strict Implication?', Journal of Symbolic Logic 28 1963, 51–71.

    Google Scholar 

  5. Hughes, G. E. and Cresswell, M. J., A New Introduction to Modal Logic (Routledge, London, 1996).

    Google Scholar 

  6. Kripke, S., 'Semantical Analysis of intuitionist Logic I', in Formal Systems and Recursive Functions, ed. J. Crossley and M. Dummett, pp. 92–130 (North-Holland, Amsterdam, 1965).

    Google Scholar 

  7. McKinsey, J. C. C. and Tarski, A., 'Some theorems about the sentential calculi of Lewis and Heyting', Journal of Symbolic Logic 13 1948, 1–15.

    Google Scholar 

  8. Prawitz, D. and Malmnäs, P., 'A survey of some connections between clasical, intuitionistic, and minimal logic', in Contributions to Mathematical Logic, eds. A. Schmidt et al., pp. 215–229 (North-Holland, Amsterdam, 1968).

    Google Scholar 

  9. Troelstra, A. S. and van Dalen, D., Constructivism in Mathematics: An Introduction, vol. 1 (North-Holland, Amsterdam, 1988).

    Google Scholar 

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Authors and Affiliations

  1. Department of Philosophy, Marquette University, Milwaukee, WI, USA

    Colin Oakes

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  1. Colin Oakes
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Oakes, C. Interpretations of intuitionist logic in non-normal modal logics. Journal of Philosophical Logic 28, 47–60 (1999). https://doi.org/10.1023/A:1004324522424

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