Rigidity

  • "Ordinarily, the word is used to describe a term, and means that the term denotes the same individual in all possible worlds"
  • Rigidity is a second-order property: it is something that is predicated of properties

"Guarino's Rigidity"

  • "These definitions bear comment because they differ from the standard use of the word ‘rigid’ in the modal logic literature.

Rigidity

  • Members of a rigid class/instances of rigid type necessarily belong to this class in all possible worlds unless they cease to exist.
    • example: an atom
      • @chatgpt (Private) While an atom can transmute into another element, it does not cease to be an atom.

Non-rigidity/semi-rigidity

  • (At least) some instances of a non-rigid class do not have to belong to that class in all possible contexts.
    • example: a mass of 4kg (artifacts might "pass through" the class, but a certain number of atoms of gold will always be 4kg)
    • example: PerformingArtist: I used to be one, but Pavement is always one.
    • example: LuxuryGood, where jewelry is always but only cars > $30k are.

anti-rigidity

  • If every individual that instantiate a given type in a particular time can cease to do so and still exists, then we call that type ANTI-RIGID
  • no instance of the property has the property necessarily
    • example: puppy

Use in ontologies

  • "The notion of rigidity is brought to bear on the task of building ontologies by the constraint that an anti-rigid property can’t subsume a rigid one"

References