Subsumption relation

In knowledge representation, object-oriented programming and design (see object-oriented program architecture), is-a (is_a or is a) is a relationship between abstractions (e.g. , ), wherein one class A is a of another class B (and so B is a of A). In other words, type A is a subtype of type B when A’s specification implies B’s specification. That is, any object (or class) that satisfies A’s specification also satisfies B’s specification, because B’s specification is weaker.

The is-a relationship is to be contrasted with the has-a (has_a or has a) relationship between types (classes); confusing the relations has-a and is-a is a common error when designing a model (e.g., a computer program) of the real-world relationship between an object and its subordinate. The is-a relationship may also be contrasted with the instance-of relationship between objects (instances) and types (classes): see "type-token distinction" and "type-token relations."

To summarize the relations, we have

Subtyping enables a given type to be substituted for another type or abstraction. Subtyping is said to establish an is-a relationship between the subtype and some existing abstraction, either implicitly or explicitly, depending on language support. The relationship can be expressed explicitly via inheritance in languages that support inheritance as a subtyping mechanism.

The following C++ code establishes an explicit inheritance relationship between classes B and A, where B is both a subclass and a subtype of A, and can be used as an A wherever a B is specified (via a reference, a pointer or the object itself).

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