There's a noticeable decrease in tension when the tires are inflated, at least with some rims. The physics of it is over my head, though.

Using a Park Tool tension meter,
A Mavic Aksium rear wheel has about 20 kgf less tension in the drive side spoke when it's at 100 psi, compared to the uninflated tire.
My old Campagnolo Vento front has 15 kgf less tension at 100 psi.

With a clincher, the air pressure inside the tire pushes evenly on the rim all the way around, trying to squeeze it into a slightly smaller diameter. The spokes stretch between the hub and the rim, as the rim gets smaller the spokes get shorter, reducing their tension.

For there to be no volume change air would have to be an incompressible fluid. It is not. If you filled your tires with water the volume would not change, but the pressure would to support the increased load. The tire would also have to be a rigid body, which is also not that case. If the pressure didn't change the loading would cause an increase in volume equal to the volume displaced by the area flattened by the contact patch. This also doesn't happen.

Volume is a term that defines quantity. In terms of the tire as a whole, the amount of air inside does not change. The air "compresses" in the tire, but the volume of air does not decrease. If you let the air out of the tire after riding, the same amount of air would come out of the tire as you originally put in, granted none leaked out. And the pressure does not change, and that is why you dont put 300psi in a tire.... 120 psi is stiff, but enough to allow slight compression to make a tire not become a solid entity. 120 psi allows the air to move upward in the tire as it rolls, and the pressure of the air inside the whole tire does not change, but at the particular spot in the tire, yes, pressure increases, but at the same time, the pressure forcing the air down toward the rim by the TOP of the tire also increases. So if you are trying to say pressure at a particular spot increases, then it does, but if you are saying the pressure inside the tire as a whole increases, then that is incorrect.

Amount of air nor pressure inside the whole tire does not change. If you want to create formula's that explain the pressures of a specific surface area, thats beyond my knowledge.

I actually thought that when the weather got better the threads would get less inane.

I was wrong.

Pretty sure your confusing volume with mass........ Volume describes the amount of space the air takes up, mass defines the amount of air present. Changing volume will change the pressure per PV=nRT.........

Ahh gotcha.

I guess you did**********??

its been a long time since physics.

correct.

Yeah, tell me about it, seems like 30 years for me, oh wait a minute....

The air in the tire presses in all directions, including inward toward the hub. I don't know jack about physics and even I can figure that out. If you have a sensitive enough instrument you would be able to measure some drop in spoke tension although it might be tiny, depending on the psi and inherent rim strength (a deep V probably compresses less than a single-wall box rim).

Jobst Brandt has discussed (argued?) this stuff in The Bicycle Wheel and in usenet discussions. You should all read his Q&A on bikes. You can learn about bikes and also get a lesson in being blunt, condescending and prickly in internet discussions - good training for Bike Forums.