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A CORRECT POLYNOMIAL TRANSLATION OF S4 INTO INTUITIONISTIC LOGIC

Published online by Cambridge University Press:  11 June 2019

RAJEEV GORÉ  and
JIMMY THOMSON
RAJEEV GORÉ
Affiliation:
RESEARCH SCHOOL OF COMPUTER SCIENCE THE AUSTRALIAN NATIONAL UNIVERSITY CANBERRA, ACT0200, AUSTRALIA E-mail: rajeev.gore@anu.edu.au
JIMMY THOMSON
Affiliation:
RESEARCH SCHOOL OF COMPUTER SCIENCE THE AUSTRALIAN NATIONAL UNIVERSITY CANBERRA, ACT0200, AUSTRALIA E-mail: jimmy.thomson@anu.edu.au
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Abstract

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We show that the polynomial translation of the classical propositional normal modal logic S4 into the intuitionistic propositional logic Int from Fernández is incorrect. We give a modified translation and prove its correctness, and provide implementations of both translations to allow others to test our results.

Keywords

03B45intuitionistic logicmodal logicpolynomial translations

Information

Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 2 , June 2019 , pp. 439 - 451
Copyright
Copyright © The Association for Symbolic Logic 2019 

References

REFERENCES

Fernández, D., A polynomial translation of s4 into intuitionistic logic, this Journal, vol. 71 (2006), no. 3, pp. 989–1001.Google Scholar
Gödel, K., Kurt Gödel: Collected Works: Volume I: Publications 1929–1936, vol. 1, Oxford University Press, New York, 1986.Google Scholar