Limiting and assisting conditions in syllogisms

The following is a case where, in my experience, no translation can be clearer than a mathematical tab. Try to read the explanation without looking at the image and/or to look at the image without reading the explanation and tell me which one is easier to grasp for you.

An Indian syllogism is based on the invariable concomitance (vyāpti, more about it here) of two elements. Due to the visible presence of one, one can hence infer the presence of the other, though it is at the moment invisible. The invariable concomitance is mono-directional and can only be applied from one element to the other. For instance, from smoke one can infer fire, whereas from fire one cannot infer smoke. This is because the set "fire" is wider than the set "smoke" (see image). And why is it the case that smoke and fire are not co-extended? Because of a limiting condition (upādhi, also called "assisting condition"). In order to be smokey, a fire needs such a limiting condition, which is hence always present when there is no smoke, but not always present when there is fire. In the case of fire, the limiting condition is that the fuel has to be partially wet. If it is absolutely dry, there is fire without smoke.

Thanks to this limiting condition, the smoke can be a reliable probans (sādhana, the instrument through which something can be established) to establish the presence of fire (sādhya, the element to be known) in a certain locus, e.g., on a smokey mountain.