Which Modal Logic is the Right One?

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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 Słupecki 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.

Original languageEnglish (US)
Pages (from-to)81-93
Number of pages13
JournalNotre Dame Journal of Formal Logic
Volume40
Issue number1
DOIs
StatePublished - 1999

All Science Journal Classification (ASJC) codes

  • Logic

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