generalizes

IRI: https://spec.industrialontologies.org/ontology/construct/generalizes

Defined In: https://spec.industrialontologies.org/ontology/core/Core/

Type: Object Property

SubProperty Of: denotes

Domain: classifier

Range: classifier

Inverse Of: specializes

Definition

relation between two classifiers such that everything classified by the latter is also classified by the former

Semi-Formal Definition:

‘c2’ generalizes ‘c1’ if and only if for every instance ‘x’, if ‘c2’ classifies ‘x’, then ‘c1’ classifies ‘x’.

Explanatory Notes

  1. Since the set designated by a classifier corresponds to a class, a subset relation between designated sets implies a subclass relation between the corresponding classes: if s2 is a subset of s1, then the class corresponding to s2 is a subclass of the class corresponding to s1. In this sense, the classifier being generalized is associated with a more specific class, while the classifier that generalizes it is associated with a more general class.

  2. For further details on what it means for a set to correspond to a class, see the FOL formalization and explanatory note for classifier.

  3. Generalizes is asymmetric and transitive. Accordingly, if one classifier generalizes a second classifier, the second does not generalize the first; and if a first classifier generalizes a second and the second generalizes a third, then the first also generalizes the third.

  4. The definition of generalizes uses ‘Set’ and related constructs which are not avalable in the current release. These constructs will be made available in the upcoming releasesAlthough Set and subset of are not explicitly available in the current release, standard set-theoretic semantics are assumed; in particular, subSetOf(s2, s1) is understood as s2 ⊆ s1.

Examples

  • UNSPSC classifier code 26101500 for engines genralizes commodity classifier code 26101507 for turboshaft engines.

Formal Axioms

First-Order Logic Definition 

generalizes(c2​, c1​) ↔ ∀x(classifies(c2​, x) → classifies(c1​, x))

First-Order Logic Axioms 

LA1: generalizes(c1, c2) ∧ designates(c1, s1) ∧ designates(c2,s2) → subSetOf(s2, s1)

LA2: generalizes(p, c) ∧ classifies(c, x)) → classifies(p, x)

Semi-Formal Natural Language Axioms

LA1: If a ‘classifier’ c1 ‘generalizes’ a ‘classifier’ c2, and c1 and c2 ‘designate’ sets s1 and s2 then s2 ‘is subset of’ s1

LA2: if p ‘generalizes’ c and c ‘classifies’ x, then p also ‘classifies’ x

Description Logic

constr:generalizes ⊑ constr:denotes

domain: constr:Classifier

range: constr:Classifier

inverse: constr:specializes

Transitive

SubPropertyOf: constr:denotes

domain: constr:Classifier

range: constr:Classifier

inverse: constr:specializes

Transitive