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Figure 1.5.
Some beliefs about George the bachelor
George was born in Boston, collects stamps.
George is the only son of Mary and Fred.
A son of someone is a child who is male.
A man is an adult male person.
A bachelor is a man who has never been married.
A (traditional) marriage is a contract between a man and a woman that is enacted by a
wedding and dissolved by a divorce. While the contract is in effect, the man (called the
husband) and the woman (called the wife) are said to be married.
A wedding is a ceremony where . . . bride . . . groom . . . bouquet . . .
and so on.
son
is supposed to mean, but its node is connected to the nodes for
child
and
male
.
Similarly, the
male
node is connected in a different way to the node for
man
. The
node for
bachelor
is connected in a complex way to the node for
marriage
and from
there, presumably, to
wedding
and
bride
. Although we may not know what any of
these terms mean in isolation, the various sorts of links given by the sentences in the
network provide a rich set of interdependencies among them.
A network like this is sometimes called a
web of belief
to emphasize that the sen-
tences do not stand alone but link to many others by virtue of the terms they use. The
job of logical entailment is to crawl over this web looking for connections among the
nodes, sensitive to the different types of links along the way. In figure 1.6 there is a
certain path from
George
to
male
, for example, that can lead to the conclusion that
George is male. If the fact that George is a bachelor is added to the web, a new set of
pathways opens, including some connections from
George
to
marriage
that were not
there before.
The logical entailments for the new sentence together with everything previously
known gives some additional answers:
George has never been the groom at a wedding.
Mary has an unmarried son born in Boston.
No woman is the wife of any of Fred's children.
These are much more like the ordinary thoughts that people would think when learn-
ing that George was a bachelor. They are not exactly poignant, of course, but if some
