% Solution to EE 4785 1996 Final Exam

% This file can be read by C-Prolog.

%
% Problem 1
%

% First, get a special case out of the way.

order([],'Undefined').

%
% The main clause: doesRepeat finds the smallest repeating list and
% lengthOf determines its length.
%

order(List,Length):-		
    doesRepeat(SubList,List),       % Get smallest repeating sublist.
    lengthOf(SubList,Length).	    % Determine its length.

%
% doesRepeat(SubList,List)
%
% succeeds if List consists of repeated occurrences of SubList.
% SubList may or may not be bound. If it's not bound then split
% will bind it to the first one or more elements of List, otherwise
% split verifies that List starts with SubList. Either way, split
% extracts the remainder of List, RestList, for a recursive call.
%

doesRepeat(SubList,List):-
    split(SubList,RestList,List),   % Split List into SubList and RestList.
    doesRepeat(SubList,RestList).   % Check if RestList consists of Sublists.

doesRepeat(_,[]).		    % End recursion when list empty.

%
% split(Left,Right,Whole)
%
% Splits list Whole into two parts, Left, a non-empty list, and Right.
% (This is similar to append, except that in append Left could be an empty
% list.)
%

split([Left],Right,[Left|Right]).

split([H|Left],Right,[H|Whole]):-
    split(Left,Right,Whole).

%
% lengthOf(List,Length)
%
% Determines the length of List.
%

lengthOf([],0).

lengthOf([_|T],C):-
    lengthOf(T,CTail), 
    C is CTail+1.


% 
% Problem 2
% 


% The file shellOAVbc.pro should be in the class directory.

:-['shellOAVbc.pro'].

% Solution to Problem 2:

r1:if thereExist(S:.isa=stock, (
    S:.cost=C and C<5 and S:.numInStock=N and N>0) ) 
   then cheapBook:=S.

r2:if 
  thereExist(S:.isa=stock, (
    S:.cost=C and C<5 and S:.title=T and S:.numInStock=N and N>0
    and
    thereExist(B:.isa=book, ( B:.title=T and B:.binding='Hardcover' ) )))
   then cheapHardCover:=S.

r3:if forAll(B:.isa=book,
             B:.series='Dilbert',
	     (
	       B:.title=T
	       and
	       thereExist(S:.isa=stock,
		 S:.title=T and S:.numInStock=N and N>0) ) )
   then haveAllDilbertBooks.

% Sample run:

% | ?- deduce(haveAllDilbertBooks,X).
% 
% X = true 
% 
% yes
% | ?- deduce(B=cheapBook and T=B:.title,_).
% 
% B = stock3
% T = Instant Expert Systems 
% 
% yes
% | ?- deduce(B=cheapHardCover and T=B:.title,_).
% 
% B = stock2
% T = More Poetry 
% 

% Sample data for above rules.

data(book1,isa,book,init).
data(book1,title,'Nontrivial Expert Systems',init).
data(book1,series,'Computer Science',init).
data(book1,binding,'Hardcover',init).

data(book2,isa,book,init).
data(book2,title,'Instant Expert Systems',init).
data(book2,series,'Computer Solutions',init).
data(book2,binding,'Paperback',init).

data(book5,isa,book,init).
data(book5,title,'More Poetry',init).
data(book5,series,'Un-Ending Verse',init).
data(book5,binding,'Hardcover',init).

data(book3,isa,book,init).
data(book3,title,'You wont survive by your wits alone',init).
data(book3,series,'Dilbert',init).
data(book3,binding,'Paperback',init).

data(book4,isa,book,init).
data(book4,title,'The Dilbert Principle',init).
data(book4,series,'Dilbert',init).
data(book4,binding,'Paperback',init).

data(stock1,isa,stock,init).
data(stock1,title,'Nontrivial Expert Systems',init).
data(stock1,cost,95.97,init).
data(stock1,numInStock,1,init).

data(stock3,isa,stock,init).
data(stock3,title,'Instant Expert Systems',init).
data(stock3,cost,4.95,init). % Wow! Includes floppy disk!
data(stock3,numInStock,10,init).

data(stock2,isa,stock,init).
data(stock2,title,'More Poetry',init).
data(stock2,cost,2.99,init).
data(stock2,numInStock,20,init).

data(stock4,isa,stock,init).
data(stock4,title,'You wont survive by your wits alone',init).
data(stock4,cost,6.95,init).
data(stock4,numInStock,10,init).

data(stock5,isa,stock,init).
data(stock5,title,'The Dilbert Principle',init).
data(stock5,cost,6.95,init).
data(stock5,numInStock,10,init).


% There are more books in the Dilbert series.


% % Problem 3
% 
% Given:
%  H1 Car problems.
%  H2 Away for a reason. 
%  H3 Weather.
% 
%  E1: Car acting strangely.
%  E2: Tow truck.
%  E3: Owns an unreliable car.
% 
%  E4: Vacation.
%  E5: Lunch.
% 
%  E6: Storm.
%  E7: Left at time of possible storm.
%  E8: Lives across river.
% 
% Rules
%
%  Since H1 could occur with any E1-E3 and two would make H1 more
%  likely the evidence should be combined with the co-combining
%  rule. The co-combining rule combines antecedents of rules, so:
% 
%    if E1 then H1.
%    if E2 then H1.
%    if E3 then H1.
% 
%  Since evidence E4 and E4 known with certainty and only one can be true:
% 
%  if E4 or E5 then H2.
% 
%  Since all three pieces of evidence are necessary for H3:
% 
%    if E6 and E7 and E8 then H3.

%
% Problem 4a
%

% thematic_role_frame1 isa thematic_role_frame
%  agent: John
%  thematic object: ball
%  destination: Jack
%  verb: throw
% 
% pa_throw1 isa pa_action
%  primitive: throw 
%  agent: John
%  object: ball
%  destination: Jack

%
% Problem 4b
%

% Since "mail" is a primitive action, the ES would "know" about the
% mailing process. For example, the ES might understand that mailing
% requires a container for the ball, stamps, a trip to a mailbox or
% post office, and at least a one-day wait before Jack receives the
% ball.
% 
% With primitive action frames an ES might estimate when Jack would
% receive the ball.

%
% Problem 4c
%

% Linguistic modifiers alter a membership function, this function maps
% elements, which have to be numbers, to the unit interval, the
% element's membership.  Elements of the set of speeds are numbers, so
% linguistic modifiers are possible. However, elements of the set of
% movies aren't numbers, so the membership function would map some other
% type of element (e.g., the movie titles) to the unit interval. It
% would be no problem, on the other hand, to provide linguistic
% modifiers for S, the set of good movie ratings, where an element of
% the set is the number of starts given by a reviewer.
%  
%
% Problem 4d
%

:-op(500,xfx,slots).
:-op(400,xfy,ako).
:-op(400,xfx,isa).


car ako roadVehicle ako personalProperty 
 slots [
  [airbag, true],
  [numCupHolders, 5]].

car1 isa car
 slots [
  [brand, gm],
  [color, arrestMeRed]].

% Syntax error since isa appears twice.
% 
% car1 isa car isa property
%  slots [
%   [brand, gm],
%   [color, arrestMeRed]].