Of COURSE they do. Just consider how they teach us to understand them.
Via "Responsible Pet Ownership":
By Linda Cole
Dogs aren't usually thought of as problem solvers. However, they are pretty good at manipulating us to get what they want. They definitely are not dumb. Dogs do think and can remember things. It's hard not to wonder what your dog is thinking about when you catch him staring off into the distance or watching TV. Of course they don't process information the same way we do – or do they?
Researchers believe the canine mind processes images in their mind via their senses. Dogs think using smells, sounds and images. It's really not unlike how we process information. When you talk to a friend on the phone, you can visualize that person's face. Our minds are full of images, smells and sounds we've learned throughout our lives. If you're thinking about buying a new car, you see the image of that car. Growling and hissing outside your bedroom window conjures up an image of two cats fighting. The smell of a neighbor's steak cooking on his grill lets you see that steak cooking. Like dogs, we get a mental picture in our mind associated with different smells, sounds and images. Although our thought process is more sophisticated, a general observation would entertain the notion that dogs think like we do.
Take for example, a dog waiting for his owner to return home. Researchers believe dogs think about us while we're gone. Since our smells are everywhere in the home, it's easy for dogs to have a mental picture of us in their minds. Look at it from your dog's point of view. Before you walk out the front door to go to work, you've engaged in a specific routine. Your dog knows you are getting ready to leave. He watches and learns what you do, and pays attention to what you've touched whether you know it or not. That's why the remote may have chew marks on it or you find your favorite book in shreds in the middle of the living room floor. It smells like you and it gave your dog a positive feeling, especially if you sat on the couch last night with him by your side as you read or watched TV.
Your dog's favorite smells are everywhere around the home, allowing him to think in images of things you do every day. In order to make himself feel better, especially if you are running late, he may “borrow” something of yours. This could act as a sort of crutch to help him get through until you arrive home.
When most dogs think of their owners, their thoughts of us are positive, which is what we want. A combination of positive and negative images can begin to confuse a dog, who then starts to exhibit behavioral problems. Yelling at your dog for something he did wrong while you were gone does nothing except to begin a reinforcement of negative feelings in him associated with you coming home. Any punishment after the fact is useless because he has no idea why you are yelling at him or punishing him. The only fair punishment is at the time the infraction took place. Dogs don't hold grudges and neither should we.
As responsible pet owners, it's up to us to understand how dogs think in order to understand how our reaction to finding something destroyed while we were gone will affect the dog. The last thing you want to do is give your dog negative thoughts connected with you returning home. The best thing to do is to count to ten, clean up the mess, and try to think like a dog and see his environment from his view. He doesn't understand how expensive your new CD was or the sentimental value of the book that was handed down to you from your great-great grandfather, or the importance of the photo album you were looking at last night that was left on the coffee table.
Your dog will search for anything with your smell on it, and it makes him feel good and happy while he waits for your return. It really isn't his fault if you forgot to put something important or expensive away. So instead of getting mad and dishing out punishment that means nothing to your dog, provide him with appropriate items he can safely snuggle with or chew on while you're gone. Give him a break. Your home is filled with your smell which keeps you in your dog's mind.
Dogs think, even though it's not on the same level as a Rhodes scholar. Most people will admit that their dog has them wrapped around their little finger. If you don't believe dogs think, then how were they able to train us so well?