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

particular relation is symmetrical.
If we know that Mia is older than Linus and we also know that Sue
is older than Mia, then using s as a name for Sue, we can reason as
follows:
older_than (s , m)
older_than (m , l)
older_than (x , y) & older_than (y , z) 
→ older_than (x , z)
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 older_than (s , l)
The conjunctive antecedent of the conditional is satisfied because
both conjuncts – the statements flanking the ampersand – are satis-
fied, so we have licence to deduce the conclusion by modus ponens,
as before. I’m sure you are quite able to discern what it is we have
proven.
This is all the terminology and symbolism we require to develop an
expert system.
13.3 KINSHIP
If you were able to follow the example deductions in the previous
section, then you already grasp the important aspects of the oper-
ations of expert systems. In fact, the example cases used to introduce
predicate notation were actually themselves miniscule expert systems.
Expert systems are formal systems which aim to encode the infor-
mation that a relevant human expert knows about a particular
domain of knowledge and to reproduce their deductive processes
given this information and some novel input. Our example expert
system is going to encode information concerning kinship relations.
The resident information of an expert system is specified in terms
of a number of conditionals. This resident information serves as the
rules of the expert system.
While we will be appealing to a logical principle – modus ponens –
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in applying the rules to make deductions, the rules themselves are not
rules of logic. Rather, the rules of the system are conditionals which
represent the information an expert knows about the relevant domain
of knowledge – in this case kinship. The logical principle will be cap-
tured in the e
ffective procedure for applying the rules.
The resident information of our kinship system is specified as
follows:
grandparent_of (x , y) & male (x) 
→ grandfather (x)
parent (x) & male (x) 
→ father (x)
parent (x) & female (x) 
→ mother (x)
parent_of (x , y) 
→ parent (x)
parent_of (x , y) 
→ child_of (y , x)
parent_of (x , y) & parent_of (y , z) 
→ grandparent_of (x , z)
The states of an expert system are sets of statements. The initial state
of our kinship system will be:
parent_of ( j , m)
parent_of (m , h)
male ( j )
male (h)
female (m)
The final thing to specify for our kinship system is the e
ffective pro-
cedure for applying rules to states.
1. Starting with the first conditional in the resident information,
check to see if there is a statement in the state which satisfies the
antecedent – i.e. check to see if any of the statements in the state
have the same logical form as the antecedent and di
ffer from it only
in substituting the variable(s) for name(s).
2. If there is a statement which satisfies the antecedent, then add
the consequent to a list of deduced statements (being careful to
substitute the variable(s) in the consequent for the same name(s) as
those in the statement(s) which satisfied the antecedent). Check for
further statements in the state which satisfy the antecedent.
3. Repeat steps 1 and 2 for each conditional in the resident informa-
tion. When this is completed, augment the original state with the
list of deduced statements and output this augmented state. Only
add a statement from the deduced list if it does not already appear
in the state.
4. Begin again with the first conditional and see if the new statements
deduced allow the deduction of further novel statements.
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5. If a state is such that none of the conditionals in the resident infor-
mation allow the deduction of statements that are not already in
the state, then halt.
Let’s apply this procedure to our initial state and see what we can
derive.