# SubsetLink

From OpenCog

The **SubsetLink** denotes extensional inheritance between two Atoms. An example of a SubsetLink would be:

Subset dog animal

For more information, see InheritanceLink#Extensional_vs_Intensional.

**SubsetLink** is also equivalent to an EvaluationLink whose PredicateNode is "Subset". Thus, for example:

SubsetLink ConceptNode: dogs ConceptNode: animals

means the same thing as:

EvaluationLink PredicateNode: Subset ListLink ConceptNode: dogs ConceptNode: animals

## Naming subsets

The SimilarityLink can be used to refine a simple subset relationship into a more complex "what kind of subset of" relationship.

## PLN Semantics

In PLN the truth value of a SubsetLink relationship actually corresponds to a conditional probability over truth values, formally:

SubsetLink <TV> A B

with

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle TV.s = \frac{\sum_x f_\wedge((\text{Member}\ x\ B).s, (\text{Member}\ x\ A).s) \times x.s}{\sum_x (\text{Member}\ x\ A).s \times x.s}}**

where (Member X Y).s measures the degree to which x is a member of concept y, which can also be represented in the AtomSpace via a MemberLink.