Those are good points, but I still find your argument problematic.

First, do you know that dogs are capable of the abstract thought necessary to represent causality? You're saying that the dog has added the belief "bark causes pain", which combines with "pain bad".

That may be how a programmer would try to represent it, since you can rely on the computational power necessary to sweep through the search space quickly and find the "pain bad" module every time a "reason to bark" comes up. But is it good as a biological model? It requires the dog to indefinitely keep a concept of a prod in memory.

A simpler biological mechanism, consistent with the rest of neurobiology, would be to just lower the connection strengths that lead to the "barking" neuron so that it requires more activation of other "barking causes" to make it fire (and thus make the dog bark). I think that's a more reasonable model of how operant conditioning works in this context.

This mechanism, in turn, is better described as lowering the "shouldness" of barking, which is ambiguous with respect to whether it's a value or belief.