# Bioinformatics Tutorial Questions 1 – 15th January 2003

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1 Οκτ 2013 (πριν από 4 χρόνια και 9 μήνες)

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Artificial Intelligence Tutorial 4
-

1a) Recall these sentences from last week’s tutorial:

(i)

All dogs are mammals

(ii)

Fido is a dog

(iii)
Fido is a mammal

(iv)

All mammals produce milk

(v)

There exists a dog which doesn’t produce milk

Using sentences (i) and (iv) in

[Note that to show you have done the step, you should use the notation from the notes, i.e., draw a
line from your two sentences to the resolved sentences, and show any substitutions you
needed to
make in
-
between the two lines]

1a) By the term “resolve”, we mean use the resolution inference rule to deduce something new from

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-
negated in (i) and negated in (iv). For other contexts, it’s important to remember that the X

different

variables. However, for this situation, we ca
n simply resolve the two
sentences to give the following:

(i) ¬dog(X)

⡮(€⁤ g(堩

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⡮(€⁤ g(堩

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fido: he produces milk. It’s important to remember to put the substitution: {X/fido} on the diagram,
so that whoever reads the diagram can understand exactly what
has occurred.

1c) Take sentences (i),(ii),(iii) and (v) as axioms about the world and show they are inconsistent with
sentence (iv). Do this by drawing a resolution proof tree. You will have to search for the correct
resolution steps at each stage to
carry out.

1d) Which steps in your proof are unit resolution steps?

1c) Remember that the resolution method performs proof by contradiction, so it derives an empty set
of clauses which we take to be the false predicate. As it has derived false, the met
hod must have
shown that there was a contradiction in the knowledge base supplied to it. So, the first thing to note
here is that we are being asked to show that (iv) is
false
. Normally, we are asked to show that
statements are
true
, in which case, we have

to
negate them

in order to use the resolution theorem
proving method. But we don’t need to negate (iv) here, as we want to derive a contradiction using (i)

oe獯汵s楯渠

didn’t use fido in the English explanation, so it’s unlikely that he’ll feature in the proof. Always bear

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S漬楮i瑨t

first resolution step, we worked out that some_animal couldn’t be a mammal (it doesn’t
produce milk, after all). If it wasn’t a mammal, then it couldn’t be a dog was decided in the next

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2) Consider the following knowledge base:

i.

boss(colin) = boris

ii.

boss(boris) =

anna

iii.

paycut(anna)

iv.

X (paycut(boss(X))

paycut(X))

Draw a resolution proof tree to show that Colin is getting a paycut. You will need to use the
demodulation inference rule.

Recall that demodulation allows us to rewrite with equalities during resolutio
n proofs. The
demodulation inference rule is

X = Y A[S]

Unify(A, S) =

S畢獴(

Ⱐ䅛奝)

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{

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D
E

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easy.

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1

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3

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easy

2

yes

3

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3

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4

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easy

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yes

2

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easy

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-
S 浥瑨潤⸠

.

3a) Which would be the most specific hypothesis that the agent would
initially

construct?

The FIND
-
S method takes the first positive example and uses that with all it’s variables ground as in

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-
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least general

(i.e., most specific) generalisation

remember that the ‘S’ inf FIND
-
p 獴慮摳s景f
‘specific’. These three are not as specific as the first one, becau

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The first hypothesis states that an exam is difficult if you use a calculator, it’s 3 hours long, Dr.
Smith is the lecturer and it’s in the spring term. It also states that the e
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