Notre Dame Journal of Formal Logic

Which Modal Logic Is the Right One?

John P. Burgess


The question, "Which modal logic is the right one for logical necessity?," divides into two questions, one about model-theoretic validity, the other about proof-theoretic demonstrability. The arguments of Halldén and others that the right validity argument is S5, and the right demonstrability logic includes S4, are reviewed, and certain common objections are argued to be fallacious. A new argument, based on work of S\lupecki and Bryll, is presented for the claim that the right demonstrability logic must be contained in S5, and a more speculative argument for the claim that it does not include S4.2 is also presented.

Article information

Notre Dame J. Formal Logic Volume 40, Number 1 (1999), 81-93.

First available in Project Euclid: 5 December 2002

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Zentralblatt MATH identifier

Primary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}


Burgess, John P. Which Modal Logic Is the Right One?. Notre Dame J. Formal Logic 40 (1999), no. 1, 81--93. doi:10.1305/ndjfl/1039096306.

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