Dealing with NOT

In one of the examples we looked at :

nice :-
  sunny,
  not_windy.

• This is really cheating
• How do we represent the not case
• Use the built in procedure not with one argument (not/1)
• So the goal, not(windy) succeeds if the goal windy fails
• It is possible that the goal is composed of sub-goals, for instance :
  not((windy, cold;hot)).
  although the arity is still 1 : goals are combined using and, or primitives
• Not : implements negation as the failure of proving that the goal is true
• Prolog assumes that everything defined in a program, or what can be derived from it is true : else : everything false - this is the closed world assumption. Hence,
  not(clever(user))
  it answers yes - even though there is no rule about the user

If I have the simple database of facts :

tel(james, 465676).
tel(mark, 332312).
tel(helen, 766786).

Then we can pose questions (queries) to Prolog in a number of different ways :

tel(mark, N)
N = 332312
yes 

tel(helen, 766786)
yes

tel(Name, 766786)
Name = helen
yes

tel(Name,Num)
Name=james
Num=465676 ;
Name=mark
Num= 332312;
...
no

Hence, the idea of obtaining information, using the reverse way. For instance, in arithmetic :

X is 2 + 18 / 5
X = 5.6
cannot say
5.6 is A + B / C  

however
X = 2 + 18 / 5
and 
A + B / C = 2 + 5 / 6
A = 2
B = 5
C = 6

Similarly, the use of the predicate not also prevents using procedures in different ways. We can, for instance, use the procedure

has_no_children(X) :- 
  not( child(_,X)).

only to check whether a certain person has no children, but cannot use it to find these people. An additional condition has to be introduced into the rule, to force X to be instantiated before executing the not( child(_,X)) goal. Hence :

has_no_children(X) :- 
  person(X),
  not( child( _,X)).

• In this case, the order of the rules is also important

  
Figure 1: A track event

• Want to define a relation better, for which, better(X,Y) is true if X finished the race before Y
• X is also better than Y, if X reached the winning post before Z, and Z reached the winning post before Y
• Could be numerous others between X and Y
• Need a more general model
• Need to consider two main cases

better(X,Y) :-
  before(X,Y).

better(X,Y) :-
  before(X,Z),
  better(Z,Y).

before(tom, tim).
before(tim, jack).
before(jack, jim).
before( jim,john).

• Recursive procedure - with a base case and a general definition