Did you find the phrase in the article "Creating a Reading Environment at Home"? The full sentence there is: Try not to use television and computers as rewards for reading (or denying them as punishment for not). This could be rephrased as: Try not to use television and computers as rewards for reading (or denying them the use of television and computers as punishment for not reading). In this case, "to deny" means: "to refuse to give (something requested or desired) to (someone)" (meaning provided by google) The other meaning of "to deny", "to refuse to admit the truth or existence of (something)" is not relevant in this case.