Binary Relations as Subsets
A binary relation is a set of ordered pairs, and a subset of a direct product (DP) of the two sets of instances which it pairwise relates.
Example: IsMarriedTo(man, woman) is a subset of the direct product of all pairs in Male x Female.
- This relation is sparse, not dense.
- It has an inverse relation IsMarriedTo(woman, man).
- The inverse (in this case) has the same name but a different argument type sequence or signature (I.e. it is polymorphic).
The rules for membership in Male, Female and IsMarriedTo must be defined very precisely.
- Question: State alternate possibilities for these rules?