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# 2 Interpretations and Models (with variables)

Suppose we had a domain with two individuals, *x* and *y*.
Suppose we had two predicate symbols *p* and *q* and three constants
*a*, *b*, and *c*. Suppose we had the knowledge base *KB* defined by
p(X) <- q(X).
q(a).

- Give one interpretation that is a model of
*KB*.
- Give one interpretation that is not a model of
*KB*.
- How many interpretations are there? Give a brief
justification for your answer.
- How many of these interpretations are models of
*KB*? Give a brief
justification for your answer.

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material, ©David Poole, Alan Mackworth and Randy Goebel, 1998