Logic Programming

1. Logic Programming PROLOG Dr. Yasser Nada Fall 2010/2011 Lecture 3 Logic Programming

2. Prolog Search Strategy • How Prolog finds answers to goals? • Prolog search for clauses from: • Top to bottom. • And left to right. • This is the same as we read the prolog program. PROLOG Logic Programming

3. Resolution and Substitution • Resolution is the process of matching the goal with the head of a clause in the program database and finding whatever substitutions that can be implied. • Substitution is replacing the variable with other variables or constants. PROLOG Logic Programming

4. And/Or Graph happy(P) • wealthy(ali). • healthy(ahmed). • wise(salem). • happy(P) :- wealthy(P). • happy(P) :- healthy(P). • happy(P) :- wise(P). • ? happy(P). • p=ali ? ; • p=ahmed? ; • p=salem ? ; • no • ? PROLOG wealthy(P) healthy(P) wise(P) p/ali p/salem p/ahmed success success success Logic Programming

5. And/Or Graph k(X) • f(a). • f(b). • g(a). • g(b). • h(b). • k(X) :- f(X), g(X). • k(X) :- f(X), h(X). • ? k(X). • X = a ? ; • X = b ? ; • X = b ? ; • no • ? PROLOG f(X) g(X) f(X) h(X) f(a) f(b) g(a) g(b) f(a) f(b) h(b) Logic Programming

6. Proof Tree or Search Tree • It is a tree that consists of: • Nodes which represents the goals. • Edges which represents the goal derivation. • The root of the tree is the query. PROLOG Logic Programming

7. Search Tree or Proof Tree • f(a). • f(b). • g(a). • g(b). • h(b). • k(X) :- f(X), g(X). • k(X) :- f(X), h(X). • ? f(a). • yes • ? f(a) Match PROLOG • If the query is grounded fact (i.e. no variables): • match the fact with the set of facts in the program. • The answer to the query is either yes or no. Logic Programming

8. Search Tree or Proof Tree • f(a). • f(b). • g(a). • g(b). • h(b). • k(X) :- f(X), g(X). • k(X) :- f(X), h(X). • ? f(X). • X = a ? ; • X = b ? ; • no • ? f(X) Match X/a X/b PROLOG • If the query is non-grounded fact (i.e. contains variables): • Find values for the variables in the query that make the query true. Logic Programming

9. Search Tree or Proof Tree • f(a). • f(b). • g(a). • g(b). • h(b). • k(X) :- f(X), g(X). • k(X) :- f(X), h(X). • ? k(X). • X = a ? ; • X = b ? ; • X = b ? ; • no • ? k(X) Match replace PROLOG f(X),g(X) f(X), h(X) X/a X/a X/b X/b g(a) g(b) h(a) h(b) Logic Programming

10. Example • big(bear). • big(elephant). • small(cat). • brown(bear). • gray(elephant). • black(cat). • dark(Z) :- black(Z). • dark(Z) :- brown(Z). PROLOG Logic Programming

11. Example • big(bear). • big(elephant). • small(cat). • brown(bear). • gray(elephant). • black(cat). • dark(Z) :- black(Z),big(Z). • dark(Z) :- brown(Z), big(Z). dark(X), big(X) X/Z X/Z PROLOG black(X),big(X) brown(X),big(X) X/cat X/bear big(cat) big(bear) Logic Programming

12. Example • big(bear). • big(elephant). • small(cat). • brown(bear). • gray(elephant). • black(cat). • dark(Z) :- black(Z). • dark(Z) :-brown(Z). big(X),dark(X) X/bear X/elephant PROLOG dark(bear) dark(elephant) Z/bear Z/bear black(bear) brown(bear) Z/elephant black(elephant) brown(elephant) Logic Programming

13. Example male(ali). male(ahmed). male(salem). father(salem, ali). father(salem, ahmed). brother(X,Y) :- father(Z,X), father(Z,Y), male(X), X \= Y. ? brother(P,A). PROLOG Logic Programming

14. Proof Tree brother(P,A) P/X, A/Y father(Z,P), father(Z,A), male(P), P\=A. PROLOG salem/Z, ahmed/P salem/Z, ali/P father(salem,A), male(ali), ali\=A. father(salem,A), male(ahmed), ahmed\=A. A/ali A/ahmed A/ali A/ahmed male(ali), ali\=ahmed. male(ali),ali\=ali. male(ahmed), ahmed\=ali. male(ahmed), ahmed\=ahmed. ali\=ahmed. ali\=ali. ahmed\=ali. ali\=ali. Logic Programming

15. Recursion • Recursion is a rule that define a relationship in terms of themselves. • You talk about someone either if you know him or you know someone who talks about him. • talk_about(A,B) :- knows(A,B). • talk_about(P,R) :- knows(P,Q), talk_about(Q,R). PROLOG Logic Programming

16. And/Or Graph Same as root tree talk_about(X,Y) X/A,Y/B X/P,Y/R PROLOG knows(X,Y) knows(X,Q) talk_about(Q,Y) Q/A,Y/B Q/P,Y/R knows(Q,Q1) talk_about(Q1,Y) knows(Q,Y) talk_about(A,B) :- knows(A,B). talk_about(P,R) :- knows(P,Q),talk_about(Q,R). Logic Programming

17. Recursion • talks about(A,B):- knows(A,B). • talks about(P,R):- knows(P,Q), talks about(Q,R). • knows(bill,jane). • knows(jane,pat). • knows(jane,fred). • knows(fred,bill). PROLOG ? talk_about(X,Y). X=bill Y=jane ? ; X=jane Y=pat ? ; X=jane Y=fred ? ; X=fred Y=bill ? ; X=bill Y=pat ? ; X=bill Y=fred ? ; X=bill Y=bill ? ; X=bill Y=jane ? ; … ? Logic Programming

18. Proof Tree Rule2 talk_about(X,Y) X/P, Y/R Rule1 X/A, Y/B knows(X,Y) knows(X,Q), talk_about(Q,Y) PROLOG X/bill,Y/jane X/jane,Y/pat X/jane,Y/fred X/fred,Y/bill Logic Programming

19. Proof Tree Not executed yet knows(X,Q), talk_about(Q,Y) X/fred,Q/bill X/bill,Q/jane PROLOG talk_about(bill,Y) talk_about(jane,Y) 4 1 X/jane,Q/pat X/jane,Q/fred talk_about(pat,Y) talk_about(fred,Y) 2 3 Logic Programming

20. Proof Tree 1 talk_about(jane,Y) Jane/A,Y/B P/jane,Y/Q PROLOG knows(jane,Y) knows(jane,Q),talk_about(Q,Y) Q/pat Q/fred Y/pat Y/fred talk_about(fred,Y) talk_about(pat,Y) 5 P/pat,Y/R pat/A,Y/B knows(pat,Y) knows(pat,Q), talk_about(Q,Y) Logic Programming

21. Proof Tree 5 talk_about(fred,Y) fred/P,Y/R fred/A,Y/B PROLOG knows(fred,Y) knows(fred,Q), talk_about(Q,Y) Q/bill Y/bill talk_about(bill,Y) bill/A,Y/B bill/P,Y/R knows(bill,Y) knows(bill,Q),talk_about(Q,Y) Q/jane talk_about(jane,Y) Y/jane Infinte loop, same as sub-goal 1 Logic Programming

22. Homework • Do Ex. 3.1 and 3.2 in your book. PROLOG Logic Programming

23. Questions PROLOG Logic Programming 23