  The `pet fish' phenomenon is often cited as a paradigm example of the
`non-compositionality' of human concept use. We show here how this phenomenon
is naturally accommodated within a compositional distributional model of
meaning. This model describes the meaning of a composite concept by accounting
for interaction between its constituents via their grammatical roles. We give
two illustrative examples to show how the qualitative phenomena are exhibited.
We go on to apply the model to experimental data, and finally discuss
extensions of the formalism.
