# PartOf Relation

A PartOf Relation is a domain independent semantic relation that is a Strict Partial Order Relation between a Component Concept if a part of a Composite Concept.

**AKA:**Meronymy, Meronym, Inclusion, Parthood, Meronomic, Part-Whole, Holonymy, ComponentOf, Subpart Relation**Context:**- It is a Directed Relation.
- It is a Strict Partial Order Relation.
- an Antisymmetric Relation; because if PartOf(
*A*,*B*) then Not PartOf(*B*,*A*). (*A car is not a part of a wheel*). - an Irreflexive Relation; because Not PartOf (
*A*,*A*) (*A wheel is not a part of a wheel*). - a Transitive Relation; because If PartOf(
*A*,*B*) And PartOf(*B*,*C*) Then PartOf(*A*,*C*). (*A wheel bearing is part of a car*).

- an Antisymmetric Relation; because if PartOf(
- It can be associated to a Semantic Relation Mention Pattern (such as: “NP is a part of NP").
- It can (typically) be a Many-to-Many Relation.

**Example(s):**- PartOf(
*wheel,car*) ⇒ True. - PartOf(
*tire,wheel*) ⇒ True. - PartOf(
*tire,car*) ⇒ True (because it is a Transitive Relation). - PartOf(
*car,car*) ⇒ False (because it is an Irreflexive Relation). - PartOf(
*car,wheel*) ⇒ False (because it is an Antisymmetric Relation). - PartOf(System Component, System).
- …

- PartOf(
**Counter-Example(s):**- an Identity Relation, such as [math]\displaystyle{ f }[/math](
*car,car*) ⇒ True. - an IsA Relation, such as [math]\displaystyle{ f }[/math](
*car,vehicle*) ⇒ True.

- an Identity Relation, such as [math]\displaystyle{ f }[/math](
**See:**Spatio-Temporal Relation, RelatedTo Relation, Mereology, Dyadic Predicate, Holonymy, Partial Order, Knowledge Representation, Synecdoche, Lexical Semantics.

## References

### 2009a

- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Mereology
- A mereological system requires at least one primitive binary relation (dyadic predicate). The most conventional choice for such a relation is Parthood (also called "inclusion"), "x is a part of y," written Pxy. Nearly all systems require that Parthood partially order the universe. The following defined relations, required for the axioms below, follow immediately from Parthood alone:

### 2009b

- (W3C, 2009) ⇒ http://esw.w3.org/topic/PartWhole
- The partOf relation is one of the basic structuring primitives of the universe. It is the foundation of Mereology, the theory of parthood relations (see e.g.
^{[1]}; which contains an extensive axiomatization of parthood by Achille Varzi, based mainly on the work of Peter Simons^{[2]}). PartOf is so basic that there is a school of thought which believes partOf and not subClass should be the central organizing relation of ontologies^{[3]}. hmm... the RoleNoun convention suggests part rather than partOf.The partOf relation is widely agreed to be a partial order; it is transitive, anti-symmetric, and reflexive. The reflexivity of partOf is, however, largely mathematical, and leads immediately to a possibly more useful irreflexive relation, properPartOf, which entails partOf (in other words, every whole is partOf itself, but nothing is a properPartOf itself).

- Another common relation in mereological theories is overlaps, the relation between two things that share at least one part. The overlaps relation is typically used to express the constraint of supplementation, that is, that two things that overlap must have at least one part that they do not share (otherwise they are the same).

- The partOf relation is one of the basic structuring primitives of the universe. It is the foundation of Mereology, the theory of parthood relations (see e.g.

- ↑ Varzi, Achille. 2003. "Mereology". In Edward N. Zalta, ed., The Stanford Encyclopedia of Philosophy
- ↑ Simons, Peter. 1987. Parts. A Study in Ontology. Oxford: Clarendon.
- ↑ Smith, Barry. 1998. The basic tools of formal ontology. In, Nicola Guarino, ed., Formal Ontology in Information Systems. IOS Pres

### 2009c

- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Meronymy
**Meronymy**(from Greek μέρος*meros*, "part" and ὄνομα*onoma*, "name") is a semantic relation specific to linguistics, distinct from the similar metonymy. A meronym denotes a constituent part of, or a member of something.^{[1]}That is,

"X" is a meronym of "Y" if

*X*s are parts of*Y*(s), or"X" is a meronym of "Y" if

*X*s are members of*Y*(s).For example,

*finger*is a meronym of*hand*because a finger is part of a hand. Similarly,*wheels*is a meronym of*automobile*.Meronymy is the opposite of holonymy. A closely related concept is that of mereology, which specifically deals with part-whole relations and is used in logic. It is formally expressed in terms of first-order logic. A meronymy can also be considered a partial order.

A meronym refers to a part of a whole. A word denoting a subset of what another word denotes is a hyponym. For example, a hyponym of

*tree*is*pine tree*or*oak tree*("a kind of tree"), but a meronym of*tree*is*bark*or*leaf*("a part of a tree").In knowledge representation languages, meronymy is often expressed as "

**part-of**".

### 2009d

- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Holonymy
- QUOTE: Holonymy (in Greek holon = whole and onoma = name) is a semantic relation. Holonymy defines the relationship between a term denoting the whole and a term denoting a part of, or a member of, the whole. That is,
- 'X' is a holonym of 'Y' if Ys are parts of Xs, or
- 'X' is a holonym of 'Y' if Ys are members of Xs.

- For example, 'tree' is a holonym of 'bark', of 'trunk' and of 'limb.'
Holonymy is the opposite of meronymy.

- QUOTE: Holonymy (in Greek holon = whole and onoma = name) is a semantic relation. Holonymy defines the relationship between a term denoting the whole and a term denoting a part of, or a member of, the whole. That is,

### 2006

- (Girju et al., 2006) ⇒ R. Girju, A. Badulescu, and Dan Moldovan. (2006). “Automatic Discovery of Whole-Part Relations.
*Computational Linguistics, 32(1). (website)*- QUOTE:This paper presents a supervised, semantically intensive, domain independent approach for the automatic detection of part-whole relations in text.

### 2000

- (Lambrix, 2000) ⇒ Patrick Lambrix. (2000). “Part-Whole Reasoning in an Object-Centered Framework." Lecture Notes in Computer Science. Springer.