Today I Learned

Some of the things I've learned every day since Oct 10, 2016

110: Combining Has-a and Is-a (Pseudo-Transitivity)

There’s a property of the interaction between the has-a and is-a relations when they are over the same set, which is somewhat similar in form — superficially, at least — to the property of transitivity. Recall that the property of transitivity says of a relation \rightarrow that if a \rightarrow b and b \rightarrow c, then a \rightarrow c.

Now denote is-a as \rightarrow and has-a as \dashrightarrow. Then this property of interaction between the two relations, which I don’t know of a name for, states

  1. If a \rightarrow b and b \dashrightarrow c, then a \dashrightarrow c.
  2. If a \dashrightarrow b and b \rightarrow c, then a \dashrightarrow c.

If you interpret what this means in plain English then the truth of this property is evident. The problem is I’ve never come across formal systems for allowing these sorts of interactions between relations, so I’m not sure if it’s something that’s already been developed. Will be looking into it more.

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