The document discusses cuts and negation in Prolog. It explains that the cut (!) operator controls backtracking by committing to choices made before it. Negation as failure allows defining predicates based on the failure of other predicates, using the fail operator combined with cut. Examples show how cut and negation as failure can be used to define preferences and conditions.

1. Cuts and Negation in Prolog

2. Overview The cut IF-Then-else Examples Negation as failure

3. The Cut Automatic backtracking is one of the most characteristic features of Prolog. There is an inbuilt Prolog predicate !, called cut, which offers a more direct way of exercising control over the way Prolog looks for solutions. Cut is simply a special atom that we can use when writing clauses. Ex: p(X) :- b(X),c(X),!,d(X),e(X).

4. consider the following piece of cut-free code: p(X) :- a(X). p(X) :- b(X),c(X),d(X),e(X). p(X) :- f(X). a(1). b(1). c(1). b(2). c(2). d(2). e(2). f(3). If we pose the query p(X) we will get the following responses: X = 1 ; X = 2 ; X = 3 ; No

5. The Cut But now suppose we insert a cut in the second clause: p(X) :- b(X),c(X),!,d(X),e(X). If we now pose the query p(X) we will get the following responses: X = 1 ; No

6. If-Then-Else In Prolog, if A then B else C is written as ( A -> B ; C). To Prolog this means: try A. If you can prove it, go on to prove B and ignore C. If A fails, however, go on to prove C ignoring B. The max predicate using the if-then-else construct looks as follows: max(X,Y,Z) :- ( X =< Y -> Z = Y ; Z = X ).

7. Negation as a Failure Predicate fail/0As its name suggests, fail is a special symbol that will immediately fail when Prolog encounters it as a goal. when Prolog fails, it tries to backtrack. Thus fail can be viewed as an instruction to force backtracking. And when used in combination with cut, which blocks backtracking, fail enables us to write some interesting programs.

8. Consider the following code: enjoys(vincent,X) :- big_kahuna_burger(X),!,fail. enjoys(vincent,X) :- burger(X). burger(X) :- big_mac(X). burger(X) :- big_kahuna_burger(X). burger(X) :- whopper(X). big_mac(a). big_kahuna_burger(b). big_mac(c). whopper(d). The first two lines describe Vincent's preferences. The last six lines describe a world containing four burgers, a, b, c, and d.

9. ?- enjoys(vincent,a). yes ?- enjoys(vincent,b). no ?- enjoys(vincent,c). yes ?- enjoys(vincent,d). yes Here, the key is the combination of ! and fail in the first line. When we pose the query enjoys(vincent,b), the first rule applies, and we reach the cut. This commits us to the choices we have made, and in particular, blocks access to the second rule. But then we hit fail. This tries to force backtracking, but the cut blocks it, and so our query fails.

10. Negation as a failure suppose that we need to write code to capture the following condition: p holds if a and b hold, or if a does not hold and c holds too. This can be captured with the help of negation as failure very directly: p :- a,b. p :- a, c. But suppose that a is a very complicated goal, it would be better to use the following program: p :- a,!,b. p :- c.

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