Rigidity
Modal Logic 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
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