0440949 - Andreas van Cranenburgh
0418838	- Berend Alberts

Legenda: & = AND, | = OR, ~ = NOT, / = exist. quant., @ = univ. quant.
         \= betekent ongelijk aan.
	 
 Het huiswerk van Week 5 bestaat uit de volgende opgaven:
 1a en 1b, 4, 19, 21 en 22. Het UNIFY algoritme van Opgave 19
 staat op Bladzijde 278.

1a. In this completely anti-standard notation the universal quantor rules over the implication/equivaqlence operator. Hence with implication and equivalence the binding order is the same.

1b.  10 ~
     20 &
     30 |
     40 ->
     50 <->
     60 @ (univ. quantor)

4.   @x, y[ Sybling(x, y) <-> x \= y & /f[ Father(f, x) & Father(f, y) ] & /m[ Mother(m, x) & Mother(m, y)] ].

19.
we have an input of x = F(x), y = G(z) and an empty theta.
UNIFY starts by checking if theta = failure, but theta is empty and this call fails, next UNIFY asks if x = y, again, this is not the case.
Then UNIFY wants to know if x or y is a variable, this again is not true, so we move on.
Then we want to know if both x and y are compounds, this is true, so UNIFY returns UNIFY(ARGS[x],ARGS[y],UNIFY(OP[x],OP[y],theta)).
UNIFY(x,z,UNIFY(F,G,[])).

21. At the point of the OCCURCHECK the UNIFY algorithm will yield failure.

22a. {A/x, B/y, B/z}
  b. {y/G(A,B), G(A,B)/y}
  c. {Father(John)/Father(x), y/John}
  d. {Father(x)/y, x/y}