# Semantic Equivalence Relation

(Redirected from Identity)

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

### 2014

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

### 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]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 ..