The Modal Formula (†) $\square \diamondsuit p \supset \square \diamondsuit \square \diamondsuit p$ Is Not First-Order Definable

  • Authors:

  • Ali Karatay

  • Affiliations:

  • Bogazici University, Bebek, Turkey 34342

  • Venue:
  • Logic, Language, and Computation
  • Year:
  • 2009

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Abstract

The formula (†) above is shown not to be first-order definable. The result is obtained by complicating the construction introduced in [4]. Two motivations are given for why the question of the first-order definability of (†) matters, one from theoretical considerations relating to modal logic, the other from applications of modal logic to philosophy, namely logic of ability. Finally a comparison with a cognate notion in the literature is given.