Side note: the opposite of cat isn't actually dog. The opposite of cat is goldfish. A goldfish loves water, is not fluffy, doesn't exterminate every bird for sport, will never knock your favorite coffee mug off your desk, not bipolar, and I'm not allergic to them.
The absence of a cat implies the absence of a cat. There could be a dog instead or a Gasplanet which has a species of conscious whales wearing silly hats rolling in the mud to communicate the need for a fruity beverage. It could be anything, it could be nothing. It is not possible, from the given facts, to come to any concrete conclusion besides that a cat, is in fact, absent.
will never knock your favorite coffee mug off your desk,
I once shared a house with someone who had a fish that would thrash around in its tank so violently it would knock things off the cabinet it was on and get water all over the floor (I had no involvement in the care of the fish, but I think its tank was too small).