### Which Modal Logic Is the Right One?

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

#### 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.

First Page:
Primary Subjects: 03B45
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1039096306
Mathematical Reviews number (MathSciNet): MR1811204
Digital Object Identifier: doi:10.1305/ndjfl/1039096306
Zentralblatt MATH identifier: 0972.03018

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