Is-A Relation

An Is-A Relation is a domain independent semantic relation that is a strict partial order relation (antisymmetric, irreflexive, transitive) between a subclass concept and a superclass concept.

• AKA: TypeOf, Subsumption, Subclass, Subtype, KindOf, MemberOf, IsAChildTo, Instance Of.
• Context:
  • It can be an InstanceOf Relation.
  • It is the Inverse Relation of the IsParentTo Relation.
  • It can be represented by:
    • an IsA Relation Mention.
    • an IsA Relation Record.
  • It can be associated to an IsSiblingTo Relation (IsPartialSiblingTo relation).
• Example(s):
  • a Hyponym Relation (between nouns).
  • a Tree of Life Relation.
    • IsA(feline, mammal) ⇒ True.
    • IsA(cat, feline) ⇒ True.
    • IsA(cat, mammal) ⇒ True; a Transitive Relation.
    • IsA(Gabor Melli, person) ⇒ True, also an InstanceOf.
  • a Family Tree Relation.
  • a Conceptual Hierarchy.
  • …
• Counter-Example(s):
  • a PartOf Relation, such as [math]\displaystyle{ f }[/math](cat,whisker) ⇒ False.
  • a PropertyOf Relation, such as [math]\displaystyle{ f }[/math](cat,black) ⇒ True.
  • [math]\displaystyle{ f }[/math](cat, plant) ⇒ False.
  • ?? [math]\displaystyle{ f }[/math](mammal, cat) ⇒ False; because it is an Antisymmetric Relation.
  • ?? any Irreflexive Relation, such as [math]\displaystyle{ f }[/math](cat, cat) ⇒ False.
• See: Incompatibility Relation, Class Concept, Hierarchy, Semantic Relation Ontology, Binary Relation, Generalization, Logic Generality, Many-to-One Relation, Instance (Computer Science), Liskov Substitution Principle, Abstractions.

---

---

References

2020

• (Wikipedia, 2020) ⇒ https://en.wikipedia.org/wiki/Is-a Retrieved:2020-12-1.
  • In knowledge representation, object-oriented programming and design (see object-oriented program architecture), is-a (is_a or is a) is a subsumption relationship between abstractions (e.g. types, classes), wherein one class A is a subclass of another class B (and so B is a superclass 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, there are: * hyperonym–hyponym (supertype–subtype) relations between types (classes) defining a taxonomic hierarchy, where ** for a subsumption relation: a hyponym (subtype, subclass) has a type-of (is-a) relationship with its hyperonym (supertype, superclass);
    • holonym–meronym (whole/entity/container-part/constituent/member) relations between types (classes) defining a possessive hierarchy, where
      • for an aggregation (i.e. without ownership) relation:
        • a holonym (whole) has a has-a relationship with its meronym (part),
      • for a composition (i.e. with ownership) relation:
        • a meronym (constituent) has a part-of relationship with its holonym (entity),
      • for a containment relation:
        • a meronym (member) has a member-of relationship with its holonym (container);
    • concept-object (type-token) relations between types (classes) and objects (instances), where
      • a token (object) has an instance-of relationship with its type (class).

2009

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Inheritance_(computer_science)
  • In object-oriented programming, inheritance is a way to form new classes (instances of which are called objects) using classes that have already been defined. The inheritance concept was invented in 1967 for Simula. [1]
  • The new classes, known as derived classes, take over (or inherit) attributes and behavior of the pre-existing classes, which are referred to as base classes (or ancestor classes). It is intended to help reuse existing code with little or no modification.
  • Inheritance provides the support for representation by categorization in computer languages. Categorization is a powerful mechanism number of information processing, crucial to human learning by means of generalization (what is known about specific entities is applied to a wider group given a belongs relation can be established) and cognitive economy (less information needs to be stored about each specific entity, only its particularities).
  • Inheritance is also sometimes called generalization, because the is-a relationships represent a hierarchy between classes of objects. For instance, a "fruit" is a generalization of "apple", "orange", "mango" and many others. One can consider fruit to be an abstraction of apple, orange, etc. Conversely, since apples are fruit (i.e., an apple is-a fruit), apples may naturally inherit all the properties common to all fruit, such as being a fleshy container for the seed of a plant.
• http://www.seop.leeds.ac.uk/entries/bolzano-logic/
  • a primitive relation between an object and an idea (an object is subsumed under an idea if that idea represents it, eg Socrates is subsumed under …

• http://www.isi.edu/isd/LOOM/PowerLoom/documentation/manual/manual_11.html
  • A subsumption relation specifies the relative generality of two concepts. A concept A subsumes a concept B if the definitions of A and B logically …

• http://coral.lili.uni-bielefeld.de/DATR/inherlexweb/node7.html
  • The subsumption relation can be understood as a relation of implication which relates more specific to more general concepts in conceptual taxonomies. In formal terms, subsumption defines a lattice, a kind of partial ordering, which may be represented as a directed acyclic graph. The hierarchical graphs defined by subsumption need not be trees, but can be more general kinds of graph in which child nodes are re-entrant, i.e. a child node may have more than one parent node. However, commonly a subsumption lattice has a core tree structure, with superimposition of more than one tree, or of other cross-classifiying structures. The subsumption relation may be seen as a generalisation relation, in that the subsumer expresses a generalisation over the subsumed.

2008

• (Corbett, 2008) ⇒ Dan R. Corbett. (2008). “Graph-based Representation and Reasoning for Ontologies.” In: Studies in Computational Intelligence, Springer. [http://dx.doi.org/10.1007/978-3-540-78293-3 10.1007/978-3-540-78293-3 doi:[http://dx.doi.org/10.1007/978-3-540-78293-3 10.1007/978-3-540-78293-3)
  • QUOTE: We say that a conceptual graph G subsumes another conceptual graph G', or G ≥ G', iff G' can be obtained by applying a finite number of canonical formation rules to G.

---