Arthur Prior used modal logics with propositional quantifiers throughout his career. As we now know, propositional quantifiers easily give rise to highly complex logics. But propositional quantifiers are syntactically simple and were philosophically attractive to Prior. We discuss how Prior put such quantifiers to work, both in his early work, and in his creation of hybrid tense logic and egocentric logic. We also discuss what we call Prior’s Ideal Language (PIL), a hybrid modal logic enriched with propositional quantifiers.

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This Time As Grandfather

  • Patrick Blackburn,
  • Torben Braüner,
  • Julie Lundbak Kofod

摘要

Arthur Prior used modal logics with propositional quantifiers throughout his career. As we now know, propositional quantifiers easily give rise to highly complex logics. But propositional quantifiers are syntactically simple and were philosophically attractive to Prior. We discuss how Prior put such quantifiers to work, both in his early work, and in his creation of hybrid tense logic and egocentric logic. We also discuss what we call Prior’s Ideal Language (PIL), a hybrid modal logic enriched with propositional quantifiers.