Quiz Logic Flashcards
p -> q ==
-p v q
Universal Quantification
“for all”, “for every”, “for each”
upsidedown A
Existential Quantification
backwards E
“for some”, “there exists”, “there is one”
Monotonic
in logic systems means can a truth ever be retracted
Converse (of an implication)
is obtained by reversing the roles of the premise and conclusion. Example p -> q becomes q -> p.
Inverse (of an implication)
is obtain by negating the premise and the conclusion. -p -> -q
Contrapositive of p -> q
-q -> -p
Converse, Inverse and Contrapositive of p -> q. Which are always equal?
Converse = q -> p
Inverse = -p -> -q
Contrapositive = -q -> -p
Contrapositive is equivalent to p -> q
Statements that are always true or false under the same conditions are called?
tautologies. example p->q == -p v q
Associative Law
(p v q) v r = ?
(p ^ q) ^ r = ?
(p v q) v r == p v (q v r) == p v (q v r)
or
(p ^ q) ^ r == p ^ (q ^ r)
Distributive Laws
p v (q ^ r) = ?
p ^ (q v r) = ?
p v (q ^ r) == (p v q) ^ (p v r)
or
p ^ (q v r) == (p ^ q) v (p ^ r)
De Morgan’s Laws
-(p ^ q) == -p v -q
or
-(p v q) == -p ^ - q
p <> q ==
(p -> q) ^ (q -> p)
or
(-p v q) ^ (-q v p)
Resolution and how it works?
method assumes that the premises are true and what we are trying to prove is false, and then try to find a contradiction. If we find a contradiction then the proof is true.
An expression is in clausal form if there is no
implication ( -> )
conjunction ( ^ )
double negation - (-)
Steps to convert to CNF?
- Remove Biconditional a b == (a -> b) ^ (b -> a)
- Remove Implication a -> b == -a v b
- Move Negation Inwards -(a v b) == -a ^ -b
or
-(a ^ b) == -a v -b
or
-(-a) == a - Apply Distribution and/or communitive law
a ^ (b v y) == (a ^ b) v (a ^ y)
or
a v (b ^ y) == (a v b) ^ (a v y)
CNF Step 1
Remove Biconditional
CNF Step 2
Remove Implication
CNF Step 3
Move Negation Inwards
CNF Step 4
Apply Distribution and/or Communitive Law
Forward Chaining
Bottom Up approach. Data driven thru knowledge base to check assertion
Backward Chaining
Top Down approach. Goal driven. Divide Goal into Sub goals. seems to use recursion
closed world assumption
means that the database contains all knowledge there is
monotonic vs non-monotonic
in a monotonic KB the conclusions can never be removed. in non-monotonic kb the assertions to be revooked