An Alternative Rule of disjunction in modal logic

@article{Williamson1991AnAR,
  title={An Alternative Rule of disjunction in modal logic},
  author={Timothy Williamson},
  journal={Notre Dame Journal of Formal Logic},
  year={1991},
  volume={33},
  pages={89-100}
}
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… CONTINUE READING
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