Representing Instances and ISA Relationships

Much of everyday knowledge is about categories — "a canary is a bird," "a bird is an animal" — and about individual members of those categories. Predicate logic and semantic-network-style representations both need clean ways to express this.

INSTANCE and ISA

Representing These Relations in Predicate Logic

INSTANCE(Tweety, Canary)
ISA(Canary, Bird)
ISA(Bird, Animal)

For all x: ISA(x, Bird) implies CanFly(x)          (with exceptions handled separately)
For all x, y, z: INSTANCE(x, y) AND ISA(y, z) implies INSTANCE(x, z)   (transitivity rule)

The transitivity rule lets the system automatically derive INSTANCE(Tweety, Bird) and INSTANCE(Tweety, Animal) from the facts above — this is exactly what makes inheritance work.

Why Distinguish INSTANCE from ISA?

Properties, Exceptions and Defaults

Inheritance through ISA/INSTANCE is extremely useful, but must allow exceptions:

For all x: ISA(x, Bird) AND NOT Abnormal(x) implies CanFly(x)
ISA(Penguin, Bird)
Abnormal(Penguin)                          (penguins are an exception)

This "default with exception" pattern (also called non-monotonic reasoning) is necessary because strict logic ("all birds fly") would be simply false the moment a single flightless bird is considered.

Practical Use

INSTANCE and ISA hierarchies are the backbone of ontologies and taxonomies used throughout AI — from simple textbook examples (canary/bird/animal) to large-scale knowledge graphs used by modern search engines and virtual assistants.