History and Foundations
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Environments and Problems
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Propositional Logic
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(q => p) | ~(q => (p | r))
is a logical consequence of the set:
{ p | q | r,
r => (p | q),
(q ^ r) => p,
~p | q | r }
.
1st Order Logic
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Exam style questions
V = { V : V starts with uppercase }
F = { coke/0, pepsi/0, competitor/1 }
P = { fizzy/1, sells_more/2 }
V = { V : V starts with uppercase }
F = { holden/0, ford/0, honda/0 main_competitor/1 }
P = { fast/1, faster/2 }
and the interpretation:
D = { commodore, laser, prelude }
F = { holden -> commodore,
ford -> laser,
honda -> prelude,
main_competitor(commodore) -> prelude,
main_competitor(laser) -> prelude,
main_competitor(prelude) -> commodore }
R = { fast(commodore) -> TRUE,
fast(laser) -> FALSE,
fast(prelude) -> TRUE,
faster(commodore,commodore) -> FALSE,
faster(commodore,laser) -> TRUE,
faster(commodore,prelude) -> TRUE,
faster(laser,commodore) -> FALSE,
faster(laser,laser) -> FALSE,
faster(laser,prelude) -> FALSE,
faster(prelude,commodore) -> FALSE,
faster(prelude,laser) -> TRUE,
faster(prelude,prelude) -> FALSE }
Show the steps of the interpretation of:
There are some students who fail. If a student fails, then either there
is a lecturer who has taught the student badly, the student is stupid.
No lecturer teaches any student badly. Therefore there is some student
who is stupid.
Resolution
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? [Y] :
! [X] :
( element(X,Y)
<=> element(X,X) )
=> ~ ( ! [X1] :
? [Y1] :
! [Z] :
( element(Z,Y1)
<=> ~ element(Z,X1) ) )
{ p(X,Y),
~p(f(X,Y),g(X,Y)),
~p(X,h(Y)) v p(X,Y),
~p(X,h(Y)) v ~p(X,X),
~p(X,Y) v p(X,X) v p(X,h(Y)) }
S = { ~r(Y) v ~p(Y),
p(b),
r(a),
p(S) v ~p(b) v ~r(S),
r(c) }
Prolog
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?-unique([cat,hat,cat,rat,mat,cat,hat],N).
yes
N = 4
You may assume that the member/2 predicate (that checks for list
membership) already exists.
?-store_input.
Enter data : cat.
Enter data : rat.
Enter data : hat.
Enter data : exit.
yes
would store the facts
user_input(cat).
user_input(rat).
user_input(hat).
in the database.
State Space Search and Production Systems
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Search Control Strategies
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PICTURE OF STATE SPACE
_ MAX
/ | \
_ _ _ MIN
/ | \ / | \ / | \
_ _ _ _ _ _ _ _ _ MAX
/|\ /|\ /|\ /|\ /|\ /|\ /|\ /|\ /|\
8 7 3 9 1 6 2 4 1 1 3 5 3 9 2 6 5 2 1 2 3 9 7 2 16 6 4
_ MAX
/ | \
_ _ _ MIN
/ | \ / | \ / | \
_ _ _ _ _ _ _ _ _ MAX
/|\ /|\ /|\ /|\ /|\ /|\ /|\ /|\ /|\
8 7 3 9 1 6 2 4 1 1 3 5 3 9 2 6 5 2 1 2 3 9 7 2 16 6 4
Knowledge Features
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Knowledge Representation
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Billy is a mountain.
Ethel is a tree.
All mountains have trees growing on them.
Billy has one tree growing on him.
Ethel grows on Billy.
Uncertainty
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[RN95 pp.413-431]
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Expert Systems
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Neural Networks
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