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(a) Deductive reasoning is based on Modus
Ponens. Write down the symbolic
expression for Modus Ponens and explain it. [2]
(b) In abductive reasoning, given that
the symbolic rule “ ”
and the consequent “b” are true, we can infer that the antecedent
“a” is true. Using an example, briefly describe a problem
when such a reasoning approach is used. [3]
(c) Given the following predicates:
study_hard(X,Y)
pass_event(X,Y)
awarded(X,Y) |
X studies hard for event Y
X passes event Y
X is awarded Y |
(i) Represent the following statements
as predicate expressions [2]
If a person studies hard, then he passes the examinations.
A person is awarded a diploma if he passes the examinations.
(ii) Given the truth of the two statements above, a reasoning technique
allows us to infer the award of a diploma to John from the fact that
he
worked hard. Name the reasoning technique and write down the
symbolic representation of this reasoning technique. [3]
(d) Given the following predicates:
father(X,Y)
spouse(X,Y)
|
X is the father of Y
X is married to Y |
And facts:
father(tom,mary)
father(tom, mike)
father(george, tom)
spouse(tom, tina)
(i) Using only the predicates given above, define a rule for
grandfather(X,Y) such that X is the grandfather of Y. [1]
(ii) State the values of Y such that grandfather(george, Y) is true.
[2]
(iii) Using only the predicates given above, define a rule mother(X,Y)
such
that X is the mother of Y. State and explain any assumptions that
you
make that will ensure that your rule is valid. [2]
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