Machine Learning - Spring 2004
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Lab experiments 11
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Program: ebl.pl
Data: dtheory1.pl, dtheory2.pl
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?- ['c:/prolog/ebl.pl'].        % load the program 
?- ['c:/prolog/dtheory1.pl'].   % load a domain theory 


1. Find a proof for the example and show it as a nested list (use print(L), because
the list is too long and Prolog does not print it completely).
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?- prove(kill(john,john),L),write(L).
[kill(john, john), [hate(john, john), [depressed(john)], possess(john, gun1), [buy(john, gun1)], weapon(gun1), [gun(gun1)]]]

L = [kill(john, john), [hate(john, john), [depressed(john)], possess(john, gun1), [buy(john, gun1)], weapon(gun1), [gun(...)]]] 


2. Show proof. Leaves are operational predicates (facts or Prolog built-in's) and nodes are rules.
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?- proof(kill(john,john)).
kill(john, john)
  hate(john, john)
    depressed(john)
  possess(john, gun1)
    buy(john, gun1)
  weapon(gun1)
    gun(gun1)
yes


3. Explanation-based generalization: generates a rule using operational predicates only.
"portray_clause(G)" is used to print the clause in a more readable format.
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?- ebg(kill(john,john),G), portray_clause(G).
kill(A, A) :-
        depressed(A),
        buy(A, B),
        gun(B).

G = kill(_G493, _G493):-depressed(_G493), buy(_G493, _G506), gun(_G506) 


4. Using a more complex domain theory (a version of the SafeToStack(X,Y) problem on page 311).
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?- ['c:/prolog/dtheory2.pl'].

Finding and printing Prolog poofs for different examples:

?- proof(safe_to_stack(o1,o2)).
safe_to_stack(o1, o2)
  lighter(o1, o2)
    weight(o1, 2)
      volume(o1, 1)
      density(o1, 2)
      2 is 1*2
    weight(o2, 5)
      isa(o2, table)
    2<5

?- proof(safe_to_stack(o1,o3)).
safe_to_stack(o1, o3)
  lighter(o1, o3)
    weight(o1, 2)
      volume(o1, 1)
      density(o1, 2)
      2 is 1*2
    weight(o3, 12)
      volume(o3, 6)
      density(o3, 2)
      12 is 6*2
    2<12

?- proof(safe_to_stack(o2,o3)).
safe_to_stack(o2, o3)
  lighter(o2, o3)
    weight(o2, 5)
      isa(o2, table)
    weight(o3, 12)
      volume(o3, 6)
      density(o3, 2)
      12 is 6*2
    5<12


5. Generating EBL rules (portray_clause(G) is used for better formatting, the standard Prolog answer is omitted):
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?- ebg(safe_to_stack(o1,o2),G),portray_clause(G).
safe_to_stack(A, B) :-
        volume(A, C),
        density(A, D),
        E is C*D,
        isa(B, table),
        E<5.

?- ebg(safe_to_stack(o1,o3),G),portray_clause(G).
safe_to_stack(A, B) :-
        volume(A, C),
        density(A, D),
        E is C*D,
        volume(B, F),
        density(B, G),
        H is F*G,
        E<H.

?- ebg(safe_to_stack(o2,o3),G),portray_clause(G).
safe_to_stack(A, B) :-
        isa(A, table),
        volume(B, C),
        density(B, D),
        E is C*D,
        5<E.

6. Extending the theory with new rules
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Here we use a simple trick. Prolog searches the database sequentially in a top-down fashion.
So, if we add a new rule in the beginning of the database, it will be applied first.
This will not restrict the original theory, because it will be still available after 
the new rule.


?- listing(safe_to_stack).  % Show the original theory

safe_to_stack(A, B) :-
        lighter(A, B).

?- proof(safe_to_stack(o2,o3)).  % Show the original proof
safe_to_stack(o2, o3)
  lighter(o2, o3)
    weight(o2, 5)
      isa(o2, table)
    weight(o3, 12)
      volume(o3, 6)
      density(o3, 2)
      12 is 6*2
    5<12

?- ebg(safe_to_stack(o2,o3),G),asserta(G).   % add a new EBG-generated rule in the beginning of the theory (note the use of assert[a]).

G = safe_to_stack(_G477, _G478):-isa(_G477, table), volume(_G478, _G589), density(_G478, _G592), _G516 is _G589*_G592, 5<_G516 

?- proof(safe_to_stack(o2,o3)).  % Show the proof with the new rule. It's shorter (more efficient).
safe_to_stack(o2, o3)
  isa(o2, table)
  volume(o3, 6)
  density(o3, 2)
  12 is 6*2
  5<12