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2002 The Modal Logic of Agreement and Noncontingency
Lloyd Humberstone
Notre Dame J. Formal Logic 43(2): 95-127 (2002). DOI: 10.1305/ndjfl/1071509431


The formula $\triangle$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 $\triangle$-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 $\triangle$A 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.


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Lloyd Humberstone. "The Modal Logic of Agreement and Noncontingency." Notre Dame J. Formal Logic 43 (2) 95 - 127, 2002.


Published: 2002
First available in Project Euclid: 15 December 2003

zbMATH: 1046.03008
MathSciNet: MR2033319
Digital Object Identifier: 10.1305/ndjfl/1071509431

Primary: 03B45

Keywords: contingency , modal logic , noncontingency , subject matters , supervenience

Rights: Copyright © 2002 University of Notre Dame


Vol.43 • No. 2 • 2002
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