Double Denormalizing in Postgres

To match the heavily denormalized format of a legacy app, I need to
take a query which gives this:

name | product | rent | own
Bob | Car | true | false
Bob | Car | false | true
Bob | Bike | false | true
Bob | Truck | true | true

and denormalize it into this:

name | rented_products | owned_products
Bob | {Car, Truck} | {Car, Truck, Bike}

I thought I could do this using array_agg, but I don't see how to do
that on a condition. In pseudocode, I'd like to do this:
SELECT
uniq(array_agg(product WHERE rent)) AS rented_products,
uniq(array_agg(product WHERE own)) AS owned_products
...

How can I achieve this? (I'm using Postgres 8.3)