## Notre Dame Journal of Formal Logic

### Which Modal Logic Is the Right One?

John P. Burgess

#### Abstract

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 Supecki 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

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

Dates
First available: 5 December 2002

http://projecteuclid.org/euclid.ndjfl/1039096306

Mathematical Reviews number (MathSciNet)
MR1811204

Digital Object Identifier
doi:10.1305/ndjfl/1039096306

Zentralblatt MATH identifier
0972.03018

#### Citation

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

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