The modal logic of agreement and noncontingency

Lloyd Humberstone

Research output: Contribution to journalArticleResearchpeer-review

16 Citations (Scopus)

Abstract

The formula ∆A (it is noncontingent whether A) is true at a point in a Kripke model just in case all points accessible to that point agree on the truth-value of A. We can think of 4-based modal logic as a special case of what we call the general modal logic of agreement, interpreted with the aid of models supporting a ternary relation, S, say, with OA (which we write instead of 4A to emphasize the generalization involved) true at a point w just in case for all points x; y, with Swxy, x and y agree on the truth-value of A. The noncontingency interpretation is the special case in which Swxy if and only if Rwx and Rwy, where R is a traditional binary accessibility relation. Another application, related to work of Lewis and von Kutschera, allows us to think of OA as saying that A is entirely about a certain subject matter.

Original languageEnglish
Pages (from-to)95-127
Number of pages33
JournalNotre Dame Journal of Formal Logic
Volume43
Issue number2
DOIs
Publication statusPublished - 1 Jan 2002

Keywords

  • Contingency
  • Modal logic
  • Noncontingency
  • Subject matters
  • Supervenience

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