meta inference rules

We now have the following meta inference rules, which seem to have a degree of completeness:

0. (implicit)

Father(Fred,Joe) => Father(Joe)

1. Symetric(A)

A(x,y) => A(y,x)

Symetric(Brother)
Symetric(Sister)
Symetric(Sibling)

Brother(Fred,Sam) => Brother(Sam,Fred)

2. Transitive(A)

A(x,y) and A(y,z) => A(x,z)

Transitive(Brother)
Transitive(Sister)
Transitive(Sibling)

Brother(Fred,Sam) and Brother(Sam,John) => Brother(Fred,John)

3. Implies(A,B)

A(x) => B(x)
A(x,y) => B(x,y)

Implies(Father,Male)
Implies(Sister,Female)

Sister(Joe,Sue) => Female(Sue)

4. ImpliesInverse(A,B)

A(x,y) => B(y,x)

ImpliesInverse(Father,Child)

Father(Fred,Joe) => Child(Joe,Fred)

5. Chain(A,B,C)

A(x,y) and B(y,z) => C(x,z)

Chain(Father,Brother,Uncle)

Father(Fred,Joe) and Brother(Joe,JJ) => Uncle(Fred,JJ)

6. QualifiedObject(A,B,C)

A(x,y) and B(y) => C(x,y)
A(y) and B(y) => C(y)

QualifiedObject(Parent,Male,Father)

Parent(Fred,Joe) and Male(Joe) => Father(Fred,Joe)

Woops! I missed one:

7. Distributed(A,B)

A(x,y) and B(x,z) => A(zy)

Distributed(Father,Brother)

Father(Fred,Joe) and Brother(Fred,Sam) => Father(Sam,Joe)