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Unary Properties & Predicates
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^universal
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 | extension/scope
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sub-section of the top-level ontology from [OntPrinc]
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[unary] PROPERTY aka. QUALITY
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("property" [OntPrinc],
"intrinsic property" [MB3],
"quality"/"quality universal" [^])
- A property is rigid if it is essential to all its instances,
ie., cannot be removed from / lost by either of them
[OntTax].
Between properties of certain kinds no subsumption (is-a) relationship
can exist. Observing this in the development of a taxonomy
can keep it more orderly (cf. the example in [OntTax]):
- an anti-rigid property can't subsume rigid properies
- an anti-external-dependency property can't subsume external-dependency properies
(eg. PARENT depends externally on CHILD)
- an anti-unity property can't subsume properies with unity conditions
(eg. topological unity: the parts of an apple;
morphological unity: the stars in a constellation;
or functional unity: the parts of a bikini)
- an IC-carrying property can't subsume non-IC-carrying properies
- a unity-condition carrying property can't subsume non-unity-condition carrying properies
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[+rigid]
[-IC] |
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[+rigid]
[+IC] |
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[-rigid]
[-indep.] |
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[-rigid]
[+indep.]
[-IC] |
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CATEGORY
| | ±independent
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Instances:
location[+indep.],
object[+indep.],
event[-indep.],
...
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| | ±independent
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Instances: person[+indep.]
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[general] ROLE
| | ±IC
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Instances: person[+indep.]
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ATTRIBUTION
| Instances: red, decomposable
- NB: color is not an attribution!
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| [original] type = IC-supplying
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supplies ("new") identity criteria (IC)
IOW, type = IC-supplying property:
A property "supplies" an IC
if it is rigid, and there's a necessary or sufficient IC for it,
and if the same IC is not already carried by all the properties (types)
subsuming that property
(it is a "new" IC)
[OntTax].
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merely carries the IC inherited from a subsuming type
[OntTax]
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| [+IC] |
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IC inherited from a [rigidly?] subsuming type (=> rigid IC)
| | Instances: student
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| [-IC] |
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formal role
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no identity criteria
| | Instances: patient, part
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carries IC inherited from a subsuming type
±rigid
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... and what about IC-supplying roles ???
- cannot be bec. non-rigid IC makes no sense ?
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| Sortal [property] = IC-carrying
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A property carrying an IC is called a sortal.
A property "carries" an IC if it is, or is subsumed by, a property supplying that IC
[OntTax].
In particular, emerging properies [^]
at higher system composition levels may be sortals
by giving raise to new identity criteria.
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Lowe's (1989) principle for well-founded ontologies/taxonomies:
«No individual can instantiate both of two sorts [Strawson 1959]
if they have different criteria of identity associated with them»
[OntPrinc]
Sorts and their ICs are the basis for developing
-> referential concepts
The definition of ontological levels (strata) can be based
on what kind of identity criteria separates the concrete particulars
at the respective level -> strata.
| Identity Criteria/Condition (IC)
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- «a principle for distinguishing and counting individual particulars»
[Strawson 1959].
- «criteria by which we are able to
distinguish and count objects of the sort in question»
[KRCR].
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predicate
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| | extension/scope
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Q: is there a [substantial] property for every predicate
(in particular, for negations and disjunctions)?
| [yes] | => ^idealism
| | [no] | => ^Bunge
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| | Unary Predicate
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Some relevant properties of unary predicates [FO 635]:
- «[A] predicate is countable if, whenever it holds for
an object x, it does not hold for a connected part of x.
... [A] predicate like PieceOfWood ... can be considered as
countable if we assume that only a detached part of a
piece of wood is itself a piece of wood»
- «A predicate is temporally stable if, whenever it
holds for an object at a time, then it must hold for the same
object at another time. According to Givón (1979),
noun-predicates like Student are temporally stable,
while verbal forms like Studies are not».
- My understanding:
While a person P is studying (studies(P,t)),
it is a student object S (student(S,t)).
S is always a student object (student(S,t')),
even when P stops studying (not studies(P,t')),
only that then P is not S any more / S ceases to exist.
- «[A] predicate is ontologically rigid if,
whenever it holds for an object,
it must hold for that object in any possible world.
In other words, if an object has a rigid property,
it cannot lose this property without losing its identity:
an apple cannot cease to be an apple will still remaining the same object,
while a student can easily have a temporary existence as a student»
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[+count]
[+stable] |
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| Sortal [predicate] = IC-supply or carry?
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Strawson's (1959) sortal predicates
are a concretization of unary logical/ structural/ taxonomic predicates:
«According to Strawson, a sortal predicate (like Apple)
"supplies a principle for distinguishing and counting individual
particulars which it collects"
whereas ...
«A predicate will be a sortal predicate if it is both
countable and temporally stable; in our proposal, unary structuring
predicates (i.e. concepts) must all be sortals» [FO 635].
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| [+rigid] |
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Substantial Sortal
=^= type (KR)
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«Within sortal predicates, a further distinction is made between
substantial sortals like Apple
and ...
«Substantial sortals are ontologically rigid, and they correspond
to what in KR terms may be called types;
...
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Instances: "apple", "color"
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| [-rigid] |
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Non-substantial Sortal
=^= role-type (KR)
=? material role
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... and
non-substantial sortals like Student,
formally capturing some ideas proposed in Wiggins (1980)» [FO 635].
...
non-substantial sortals are non-rigid, and they correspond to what have been called
role-types (Sowa, 1988)» [FO 636].
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Instances: "student"
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discriminating but non-sortal
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...
whereas a non-sortal predicate like Red
"supplies such a principle only for particulars
already distinguished, or distinguishable, in accordance
with some antecedent principle or method."» [FO 635].
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= "already distinguished" ?
= with inherited IC ?
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Instances: "physical object", "gold"
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characterizing pred.
=? attribution
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= not "already distinguished" ?
= without IC ?
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Instances: "red", "studies"
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Instances: "entity"
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