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Is there a standard symbol for "is a"?

Simple question, is there an accepted standard symbol for an "is a" relationship? I know in math there are the ⊆ - subset, ⊂ - proper subset, ∈ - element of symbols, do I just use one of those or is there a more code specific one to use?

This came up while trying to respond to a statement written as sedan === car and I wondered what a better symbol to use for the === was.

Solution

  • As far as I understand, you are looking for something like intensional membership symbol. You don't want to use traditional set-theory "∈" due to its extensional nature.

    Right, set-theory "∈" (as well as the set theory itself) is extensional due to these axioms:

    1. ∀P∃A∀X (X∈A ⇔ P(X)) — comprehension axiom (in a very naive form),
    2. ∀A∀B (∀X (X∈A ⇔ X∈B ) ⇔ A=B ) — axiom of extensionality.

    In set theory jargon, one might write something like this:

    • my_sedan ∈ Cars, or

    • my_sedan ∈ {x : Car(x)}, or

    • Car(my_sedan).

    There is not accepted standard symbol for "intensional membership". You can try:

    1. my_sedan : Car — in a type theory manner;

    2. my_sedan η Car — as used here or here;

    3. my_sedan a Car — as in RDF 1.1 Turtle Syntax;

    4. my_sedan cop. Car.