# Semantic Equivalence Relation

A Semantic Equivalence Relation is a semantic relation that is an equivalence relation (that tests whether two referencers refer to the name concepts).

**AKA:**Identity Relation, Coreference Relation.**Context:**- It can be identified for two or more entities by a Coreference Identification Task.
- It can test whether two Concept References refer to the name Concepts.
- It can range from being an Unweighted Semantic Equivalence Relation to being a Weighted Semantic Equivalence Relation.
- It can define a Semantic Equivalence Class.

**Example(s):**- “
*Phosphorus**(the morning star) refers to the same celestial body as*Hesperus*(the evening star).".* - ...

- “
**Counter-Example(s):****See:**Relation, Reflexive Relation, Intersection Relation, Ship of Theseus, Identity of Indiscernibles, Identity And Change, Entity Continuity.

## References

### 2014

- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Identity_(philosophy) Retrieved:2014-7-27.
- In philosophy,
**identity**, from ("sameness"), is the relation each thing bears just to itself.^{[1]}^{[2]}The notion of identity gives rise to many philosophical problems, including the identity of indiscernibles (if*x*and*y*share all their properties, are they one and the same thing?), and questions about change and personal identity over time (what has to be the case for a person*x*at one time and a person*y*at a later time to be one and the same person?).It is important to distinguish the philosophical concept of identity from the more well-known notion of identity in use in psychology and the social sciences. The philosophical concept concerns a

*relation*, specifically, a relation that*x*and*y*stand in if, and only if they are one and the same thing, or*identical to*each other (i.e. if, and only if*x*=*y*). The sociological notion of identity, by contrast, has to do with a person's self-conception, social presentation, and more generally, the aspects of a person that make them unique, or qualitatively different from others (e.g. cultural identity, gender identity, national Identity, online identity and processes of identity formation).

- In philosophy,

### 2009

- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Equality_(mathematics)
- Equality is the paradigmatic example of the more general concept of equivalence relations on a set: those binary relations which are reflexive, symmetric, and transitive. The relation of equality is also antisymmetric. These four properties uniquely determine the equality relation on any set S and render equality the only relation on S that is both an equivalence relation and a partial order. It follows from this that equality is the smallest equivalence relation on any set S, in the sense that it is a subset of any other equivalence relation on S.
- An equation is simply an assertion that two expressions are related by equality.
- The symbol "=" is sometimes used for relations other than equality. For example, the statement T(n) = O(n2) means that T(n) grows at the order of n2. Despite the notation, the statement is better understood as asserting a set membership: O(f(n)) is formally the set of all functions on the positive integers that, for large [math]\displaystyle{ n }[/math], grow no faster than f(n). In particular, since membership, unlike equality, is not symmetric, it is meaningless to write O(n2) = T(n). See Big O notation for more details.

### 2003

- (Hollink et al., 2003) ⇒ Laura Hollink, Guus Schreiber, Jan Wielemaker, and Bob Wielinga. (2003). “Semantic Annotation of Image Collections.” In: Proceedings of the Workshop on Knowledge Markup and Semantic Annotation (KCAP 2003).
- ABSTRACT: In this paper we discuss a tool for semantic annotation and search in a collection of art images. Multiple existing ontologies are used to support this process, including the Art and Architecture Thesaurus, WordNet, ULAN and Iconclass. We discuss knowledge-engineering aspect such as the annotation structure and links between the ontologies. The annotation and search process is illustrated with an application scenario. 1.
- QUOTE: ... 3.4 Searching for an image The tool provides two types of semantic search ... Because the ontologies contain an equivalence relation between Venus (as a Roman deity, not the planet nor the tennis player) and Aphrodite, the search tool is able to retrieve images for which there is ..