General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

Definition 632 A query is a list of ProLog terms called goals. Write as ?- A1, . . ., An.,
if Ai are terms.
Problem: Knowledge bases can be big and even infinite.
Example 633 The the knowledge base induced by the program
nat(zero).
nat(s(X)) :- nat(X).
is the set {nat(zero), nat(s(zero)), nat(s(s(zero))), . . .}.
Idea: interpret this as a search problem.
state = tuple of goals; goal state = empty list (of goals).
next(〈G, R1, . . . Rl〉) := 〈σ(B1), . . ., σ(Bm, R1, . . . , Rl)〉 (backchaining) if there is a rule
H:-B1,. . ., Bm. and a substitution σ with σ(H) = σ(G).
Example 634 (Continuing Example 633) ?- nat(s(s(zero))).
?- nat(s(zero)).
?- nat(zero).
Yes
c○: Michael Kohlhase 506
This search process has as action the backchaining rule, which is really just a clever combination
of the inference rules from Definition 630 applied backwards.
The backchaining rule takes the current goal G (the first one) and tries to find a substitution
σ and a head H in a program clause, such that σ(G) = σ(H). If such a clause can be found, it
replaces G with the body of the rule instantiated by σ.
But we can extend querying from simple yes/no answers to programs that return values by simply
using variables in queries. In this case, the ProLog interpreter returns a substitution.
Querying the Knowledge base (continued)
If a query contains variables, then ProLog will return an answer substitution.
has_wheels(mybmw,4).
has_motor(mybmw).
car(X):-has_wheels(X,4),has_motor(X).
?- car(Y)
?- has_wheels(Y,4),has_motor(Y).
Y = mybmw
?- has_motor(mybmw).
Y = mybmw
Yes
If no instance of the statement in a query can be derived from the knowledge base, then the
ProLog interpreter reports failure.
?- nat(s(s(0))).
?- nat(s(0)).
?- nat(0).
FAIL
No
c○: Michael Kohlhase 507
With this, we can already do the “fallible Greeks” example from the introduction.
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