Semantic Equivalence Relation

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, Personal Identity, Identity (Social Science), Cultural Identity, Gender Identity, National Identity, Entity Continuity.

References

(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).

↑ Stanford Encyclopedia of Philosophy: Identity, First published Wed Dec 15, 2004; substantive revision Sun Oct 1, 2006.
↑ The Cambridge Dictionary of Philosophy, 2nd Edition, CUP: 1995

(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]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.

(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 ..