%% mystery.lp -- Chapter 6, Section 6.2.2
%% Last Modified: 1/30/14
%% Vinny has been murdered, and Andy, Ben, and Cole are
%% suspects. Andy says he did not do it. He says that Ben was
%% the victim's friend but that Cole hated the victim. Ben
%% says he was out of town the day of the murder, and besides he
%% didn't even know the guy. Cole says he is innocent and he saw
%% Andy and Ben with the victim just before the murder.
%% Assuming that everyone --- except possibly for the murderer ---
%% is telling the truth, use ASP to solve the case.

person(andy).  
person(ben).  
person(cole).  
person(vinny). 

%% Andy says:
says(andy, murderer(andy), 0).       %% He didn't do it.
says(andy, hated(cole, vinny), 1).   %% Cole hated Vinny.
says(andy, friends(ben, vinny), 1).  %% Ben and Vinny were friends.

%% Ben says:
says(ben, out_of_town(ben), 1).     %% He was out of town.
says(ben, know(ben, vinny), 0).     %% He didn't know Vinny. 

%% Cole says:
says(cole, innocent(cole), 1).        %% He is innocent.
says(cole, together(andy, vinny), 1). %% He saw Andy and Ben
says(cole, together(ben, vinny), 1).  %% with the victim.

%% Everyone, except possibly for the murderer, is telling the truth:
holds(S) :- says(P,S,1),  
            -holds(murderer(P)).
-holds(S) :- says(P,S,0),
             -holds(murderer(P)).
      
%% Normally, people aren't murderers:       
-holds(murderer(P)) :- person(P),                    
                       not holds(murderer(P)).
                       
%% Relation together is symmetric and transitive:
holds(together(A,B)) :- holds(together(B,A)). 
holds(together(A,B)) :- holds(together(A,C)),
	                    holds(together(C,B)).
	                    
%% Relation friends is symmetric:
holds(friends(A,B)) :- holds(friends(B,A)).

%% Murderers are not innocent:
:- holds(innocent(P)),                       
   holds(murderer(P)). 
   
%% A person cannot be together with someone who is out of town:
:- holds(out_of_town(A)),                    
   holds(together(A,B)).  
   
%% Friends know each other:
:- -holds(know(A,B)),                        
    holds(friends(A,B)).
    
%% A person who was out of town cannot be the murderer:
:- holds(murderer(P)),
   holds(out_of_town(P)).                    

%% For display:
murderer(P) :- holds(murderer(P)).           

% The murderer is either andy, ben or cole, (exclusively):
holds(murderer(andy)) | holds(murderer(ben)) | holds(murderer(cole)). 

%% To use the choice rule, replace the disjunction with:
%% 1{holds(murderer(andy)); holds(murderer(ben)); holds(murderer(cole))}1.