Can’t we solve Hallucinations by introducing a Penalty during Post-training?

Currently, reasoning models like Deepseek R1 use outcome-based reinforcement learning, which means it is rewarded 1 if their answer is correct and 0 if it's wrong. We could very easily extend this to 1 for correct, 0 if the model says it doesn't know, and -1 if it's wrong. Wouldn't this solve hallucinations at least for closed problems?