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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.

Solution to part (a)

Solution to part (b)

Solution to part (c)

Solution to part (d)