Minds and Computers : An Introduction to the Philosophy of Artificial Intelligence

Exercise 13.4
Before reading on, determine what new statements, if any, can
be deduced on the second pass through the conditionals in the
resident information. What about the third pass?
The second pass through the conditionals in the resident information
will allow us to deduce three novel statements:
grandfather (j)
father (j)
mother (m)
A third pass generates only redundant statements – statements which
are already in our generated state – so we halt.
Exercise 13.5 (Challenge)
Augment the initial state of our kinship system with the
statements:
parent_of (m , j)
female (j)
di
ff ( j , h)
di
ff (m , h)
and add the following conditionals to the resident
information:
parent_of (x , y) & parent_of (x , z) & di
ff (y , z) → siblings
(y , z)
siblings (x , y) & male (x) 
→ brother (x)
siblings (x , y) & female (x) 
→ sister (x)
siblings (x , y) 
→ siblings (y , x)
Apply the rules to generate all the statements you can. Do
things appear a little strange? Why?
13.4 EXPERT SYSTEMS
The example expert system of the previous section is greatly simpli-
fied but, nonetheless, it is clear that it is able to capture the deductive
process that we engage in when reasoning about kinship relations.
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It may seem cumbersome and artificial compared to our thought
processes but this is only because the kind of reasoning we do when
told that someone is a female parent is rapid and automatic. We don’t
need to explicitly apply a rule to determine that the person in ques-
tion is a mother – this is simply something we automatically under-
stand when we understand that they are a female parent. This doesn’t,
however, speak against the claim that this implicit understanding is
governed by just such methods.
In fact, if you are asked to determine what relation to you your
mother’s sister’s daughter’s husband is, you are likely to have to think
more explicitly about the kinship relations involved, following rules
very much like the ones we encoded in the previous section.
Interesting expert systems are, of course, considerably more
complex than our example. Our kinship system has very little resident
information and appeals to only one logical principle – modus ponens.
More complicated expert systems will involve considerably more resi-
dent information and will appeal to numerous logical principles in
applying rules.
Consequently, we will often want to generate a bottom-up search
to determine whether or not a particular statement is included in any
generated state. In such cases we begin with just the statement we are
interested in deriving and work backwards through the rules, consid-
ering not entire states but, rather, just those statements which must be
included in a state in order for us to have derived the statement(s) at
the previous iteration. If a statement at a node is included in the initial
state, then we can strike it o
ff at the next iteration. If we get to a node
where nothing needs to be included in the state to prove the statement
at the previous iteration – i.e. the statement(s) we did need to gener-
ate the state we are interested in have been shown to be included in the
initial state – then the search ends in success.
Figure 13.1 demonstrates a bottom-up search for the state father
(j) in our kinship system. At the first iteration, we work backwards
through the available rules to determine that the only way to generate
father (j) is if we have parent (j) and male (j).
At the second iteration, there are three branches, representing the
three statements which would allow us to generate parent (j). The left-
hand and right-hand branches end in failure since neither parent_of
( j , j) nor parent_of (j , h) are in the initial state and there is no rule
which allows us to generate parent_of statements.
The middle branch continues since we have parent_of (j , m) in the
initial state so we discharge this statement at the next descendant
node, leaving only male (j) to prove. At the next iteration we discharge
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this last statement as it too is in our initial state, leaving nothing (the
empty set) to prove. So a search path down the middle branch ends in
success and we read the derivation o
ff by following the branch back
up to the root node.