An alternative rule of disjunction in modal logic

Notre Dame Journal of Formal Logic 33 (1):89-100 (1991)
Lemmon and Scott introduced the notion of a modal system's providing the rule of disjunction. No consistent normal extension of KB provides this rule. An alternative rule is defined, which KDB, KTB, and other systems are shown to provide, while K and other systems provide the Lemmon-Scott rule but not the alternative rule. If S provides the alternative rule then either —A is a theorem of S or A is whenever A -> ΠA is a theorem; the converse fails. It is suggested that systems with this property are appropriate for handling sorites paradoxes, where D is read as 'clearly*. The S4 axiom fails in such systems
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DOI 10.1305/ndjfl/1093636011
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Denis Bonnay & Paul Égré (2009). Inexact Knowledge with Introspection. Journal of Philosophical Logic 38 (2):179 - 227.
Rosalie Iemhoff (forthcoming). On Rules. Journal of Philosophical Logic:1-15.
Timothy Williamson (1994). Non-Genuine MacIntosh Logics. Journal of Philosophical Logic 23 (1):87 - 101.

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