% =================================================================
% == ==
% == An Introduction to ARTIFICIAL INTELLIGENCE ==
% == Janet Finlay and Alan Dix ==
% == UCL Press, 1996 ==
% == ==
% =================================================================
% == ==
% == chapter 2, pages 37-38: certainty factors ==
% == ==
% == Prolog example, Alan Dix, August 1996 ==
% == ==
% =================================================================
mb(foggy,'air is moist',0.5).
md(foggy,'air is moist',0.1).
mb(foggy,'poor visibility',0.7).
md(foggy,'poor visibility',0.0).
% The predicate cf(H,E,CF) calculates the certainty factor of
% an hypothesis H given a single evidence E
cf(H,E,CF) :-
mb(H,E,MB),
md(H,E,MD),
CF is MB-MD.
% There are two versions of the predicates.
% The first version of each mb0 and md0 uses the formulae
% to calculate the combined measure of belief/disbelief
% The second version of each mb and md, adds in the extra
% rule which says that each is 0 if the other is 1.
% If we coded this with a single predicate, then
mb0(H,E1,E2,MB) :-
mb(H,E1,MB1),
mb(H,E2,MB2),
MB is MB1 + MB2*(1-MB1).
md0(H,E1,E2,MD) :-
md(H,E1,MD1),
md(H,E2,MD2),
MD is MD1 + MD2*(1-MD1).
mb(H,E1,E2,0) :- md0(H,E1,E2,1).
mb(H,E1,E2,MB) :- not md0(H,E1,E2,1), mb0(H,E1,E2,MB).
md(H,E1,E2,0) :- mb0(H,E1,E2,1).
md(H,E1,E2,MD) :- not mb0(H,E1,E2,1), md0(H,E1,E2,MD).
% Note the trick here, mb/3 are the facts and mb/4 is
% the calculation. We are usingh the same predicate name
% with different numbers of arguments.
% the certainty factor calculations are identical to cf/3
cf(H,E1,E2,CF) :-
mb(H,E1,E2,MB),
md(H,E1,E2,MD),
CF is MB-MD.
% RUNNING THIS CODE
%
% First of all check the certainty factor calculations for
% single evidences:
% cf(foggy,'air is moist',CF).
% cf(foggy,'poor visibility',CF).
% then try to combine evidence:
% cf(foggy,'air is moist','poor visibility',CF).
%
% You can also examine the calculated measures of belief and
% disbelief given the combined evidence:
% mb(foggy,'air is moist','poor visibility',MB).
% md(foggy,'air is moist','poor visibility',MD).
%
% MORE EVIDENCE
%
% We can do the same for a whole list of evidences
% Obviously more types of evidence would need to be included
% In the database for this to be useful!
mb0_list(H,[],0).
mb0_list(H,[E|Rest],MB) :-
mb(H,E,MBe),
mb_list(H,Rest,MBrest),
MB is MBe + MBrest*(1-MBe).
md0_list(H,[],0).
md0_list(H,[E|Rest],MD) :-
md(H,E,MDe),
md_list(H,Rest,MDrest),
MD is MDe + MDrest*(1-MDe).
mb_list(H,Elist,0) :- md0_list(H,Elist,1).
mb_list(H,Elist,MB) :- not md0_list(H,Elist,1), mb0_list(H,Elist,MB).
md_list(H,Elist,0) :- mb0_list(H,Elist,1).
md_list(H,Elist,MD) :- not mb0_list(H,Elist,1), md0_list(H,Elist,MD).
cf_list(H,Elist,CF) :-
mb_list(H,Elist,MB),
md_list(H,Elist,MD),
CF is MB-MD.
%
% check with a few examples that 'cf_list(H,[E1,E2],MB)' gives the same
% answer as 'cf(H,E1,H2,MB)'