% TIME PERIODS

time(0..4).
next(T1,T2) :- 	time(T1),
		time(T2),
		T2=T1+1.


% OBJECTS OF OUR UNIVERSE (including fluents)

agent(jill).
agent(gwen).
agent(ben).
agent(marshall).
agent(erica).

object(bat).
object(glove).

truth_value(1).
truth_value(0).



fluent(i, owns(A,O)) 	:- agent(A),object(O).
fluent(i, stolen(A,O)) 	:- agent(A),object(O).
fluent(i, missing(O)) 	:- object(O).

fluent(n,at_practice(A))	:- agent(A).
fluent(i,opportunity(A,O))	:- agent(A),object(O).
fluent(n,noticed(missing(O)))	:- agent(A),object(O).
fluent(i, weak_suspect(A,O)) 	:- agent(A), object(O).
fluent(i, strong_suspect(A,O))	:- agent(A), object(O).
fluent(i, suspect(A,O)) 		:- agent(A),object(O).
fluent(i,strong_suspect_exists).


%INTEGRITY CONSTRAINTS
	:- 	fluent(X,F), 
   		time(T), 
		holds(F,T,1),
		holds(F,T,0).	

% INERTIA RULES
	holds(F,T2,1) 	:-	next(T1,T2),
			fluent(i,F),
			holds(F,T1,1),
			not holds(F,T2,0).


	holds(F,T2,0) 	:- 	next(T1,T2),
			fluent(i,F),
			holds(F,T1,0),
			not holds(F,T2,1).


% Close World Assumption
holds(stolen(A,O),0,0) 	:- agent(A),object(O),not holds(stolen(A,O),0,1). 
holds(missing(O),0,0) 	:- object(O),not holds(missing(O),0,1).
holds(owns(A,O),0,0) 	:- agent(A),object(O),not holds(owns(A,O),0,1).
holds(suspect(A,O),0,0) :- agent(A),object(O),not holds(suspect(A,O),0,1).
holds(at_practice(A),0,0):-agent(A),not holds(at_practice(A),0,1).
holds(opportunity(A,O),0,0):-agent(A),object(O),not holds(opportunity(A,O),0,1).
holds(noticed(missing(O)),0,0):-object(O),not holds(noticed(missing(O)),0,1).
holds(weak_suspect(A,O),0,0):-agent(A),object(O),not holds(weak_suspect(A,O),0,1).
holds(strong_suspect(A,O),0,0):-agent(A),object(O),not holds(strong_suspect(A,O),0,1).
holds(strong_suspect_exists,0,0):-not holds(strong_suspect_exists,0,1).


% MAIN PROGRAM
holds(owns(jill,bat),0,1).
holds(owns(gwen,glove),0,1).
holds(at_practice(jill),1,1) :- time(T).
holds(at_practice(gwen),1,1) :- time(T).
holds(at_practice(ben),1,1) :- time(T).
holds(at_practice(marshall),1,1) :- time(T).

holds(opportunity(A,O),T,1):- 
				agent(A),
				object(O), 
				time(T),
				holds(at_practice(A),T,1),
				holds(noticed(missing(O)),T,1).

holds(opportunity(A,O),T,0):- 
				agent(A),
				agent(A2),
				object(O), 
				time(T),
				not holds(stolen(A,O),T,1),
				holds(stolen(A2,O),T,1).
				
							
holds(missing(O),T,0):-
				agent(A),
				object(O), 
				time(T),
				holds(stolen(A,O),T,1).


holds(weak_suspect(A,O),T,1) :- 
				agent(A),
				object(O), 
				time(T), 
				holds(opportunity(A,O),T,1),
				holds(missing(O),T,1),
				not holds(strong_suspect(A,O),T,1),
				not holds(owns(A,O),T,1).
				
holds(weak_suspect(A,O),T,0) :- 
				agent(A),
				object(O), 
				time(T),
				holds(missing(O),T,0). 

 				
				
holds(strong_suspect(A,O),T,1) :- 
				agent(A),
				object(X),
				object(O), 
				time(T), 
				holds(opportunity(A,O),T,1),
				holds(missing(O),T,1),
				holds(stolen(A,X),T,1),
				not holds(owns(A,O),T,1).

holds(strong_suspect_exists,T,1)   :- 
				agent(A),
				object(O), 
				time(T),
				holds(strong_suspect(A,O),T,1).

holds(suspect(A,O),T,1) :- 
				agent(A),
				object(O), 
				time(T),
				holds(weak_suspect(A,O),T,1),
				not holds(strong_suspect_exists,T,1).

holds(suspect(A,O),T,1) :- 
				agent(A),
				object(O), 
				time(T),
				not holds(stolen(A,O),T,1),
				holds(strong_suspect(A,O),T,1).
				
holds(suspect(A,O),T,0) :- 
				agent(A),
				%agent(A2),
				object(O), 
				time(T),
				holds(strong_suspect_exists,T,1),
				%holds(stolen(A2,O),T,1),
				not holds(strong_suspect(A,O),T,1).
				


				

% EXECUTION-1
% NOTHING IS MISSING, SO IF WE RUN ONLY THIS EXECUTION, 
% WE DO NOT FIND ANYONE AS A SUSPECT.

% EXECUTION-2
% AT TIME=1, BAT IS MISSING WHICH IS OWNED BY JILL.
holds(missing(bat),1,1).

% ONCE WE NOTICE THAT THE BAT IS MISSING AT TIME=1, EVERYONE WHO
% IS AT PRACTICE HAD THE OPPORTUNITY TO STEAL THE BAT. THIS EXCLUDES
% THE BAT'S OWNER 'JILL'.
% BECAUSE 'ERICA' IS NOT PRESENT AT PRACTICE AT THIS TIME, SHE IS NOT 
% CONSIDERED AS A SUSPECT
holds(noticed(missing(bat)),1,1).

% EXECUTION-3
% AT TIME=3, GLOVE (OWNED BY 'GWEN') IS MISSING AND EVERYONE INCLUDING 
% 'JILL' HAD AN OPPORTUNITY.
holds(missing(glove),2,1).
holds(at_practice(erica),2,1).
holds(at_practice(jill),2,1).
holds(at_practice(gwen),2,1).
holds(at_practice(ben),2,1).
holds(at_practice(marshall),2,1).

% NOW THAT 'ERICA' IS ALSO PRESENT AT PRACTICE, SHE AUTOMATICALLY BECOMES 
% THE SUSPECT FOR THE GLOVE BUT NOT THE BAT.
holds(noticed(missing(glove)),2,1).

% EXECUTION-4

% ONCE MARSHALL IS CAUGHT FOR STEALING THE GLOVE, HE BECOMES THE "ONLY" SUSPECT 
% FOR STEALING THE BAT. BEFORE CONCLUDING THIS, IT IS VERIFIED THAT MARSHALL 
% HAD AN OPPORTUNITY TO STEAL THE BAT(PRESENT AT PRACTICE). NOW THAT MARSHALL HAS 
% HISTORY OF STEALING, MAKES US CONCLUDE DECISIVELY THAT HE IS THE ONLY SUSPECT.
holds(stolen(marshall,glove),3,1).