202      líí. PROLOG
7 Negation and Nonmonotonic Logic
203
.41.
Exercises
1. Show tiiat no selection rule that always chooses the same literal from each goal clause can. be fair.
(Hint: Consider the program P with three clauses:
(1) r :-- p,q.      (2) p.- p.      (3) q :- g. )•
2. Describe a fair generalized selection rule arid prove that It is Mr,
(Hint: Always choose the first literal to appear 1b the proof so far that has not yet been chosen.)
3. Complete the proof of Lemma 6,8,
4. 'Verify that the relation = defined in the proof of Theorem 6.10 is an equiv-
alence relation,
5, Verify that the in tiic prooi oi • t.--
6. ••.->'.,, i
itisfie
.10 wi
)rancl mow
Jí      I   •<)-     / 11
mar approac
r '   I    _        - I,,'.
ř ř
revise o 1 n
oa! clauses. (Hint:
=tr?n
>r »tl.
10. Give an example of a general program P such that Comp(P) (and hence P) is satislabie but CWA(P') is not,
11. Give an example of a general program P such that cwa(P) (and heno-is satisfiahie but CoinpiP) is not.
12. Give an example of a satisfiahie general program P such that m-t'her Comp(F) aor CWA is satisfiahie.
s • ll
o
ODí"
imei
primarily with the prepositional r*or negation in. PROLOG, this means tnat we are
t,  •<     •     •        < . i ■     )      , • *
C     <      ■>.- "    .   s'  .   •      »      t ' ,
PROLOG (although it is not precisely the same as tl ay's