**Go backward to **Solution to part (c)

**Go up to **2 Interpretations and Models (with variables)

## Solution to part (d)

*How many of these interpretations are models of **KB*? Give a brief
justification for your answer.

There are the same number of possible *phi*'s (the KB doesn't
constrain this).

For each of the *phi*'s, there are two values for the
*pi(q)*. (Depending on whether *q* of the other individual (whichever
of *x* and *y* isn't denoted by *a*) is true or
false).

For the case where *q* is true of both individuals, *p* must also be
true of both individuals. There are thus *8* interpretations where *q*
is true of both individuals.

For the case where *q* is true of just one individual (it must be the
individual denoted by *a*), *p* must be true of that individual and
can either be true or false of the
other individual. There are thus 16 interpretations where *q*
is true of one individual.

Thus there are *8+16=24* models of KB.

Computational
Intelligence online
material, ©David Poole, Alan Mackworth and Randy Goebel, 1998