I think you confused the term "inverse logic". You are simply confused about the power supply requirements of the EC51918 chip. After reviewing the data sheet, it appears like V- must be at -3V, relative to the ground pins. So, you could supply V- with 0V and VGND/AGND with +3V, or V- with +12V and VGND/AGND with +15V. I you reverse them, you'll probably destroy the part.
As far as the IC is concerned, all it needs is a differential voltage from V- to VGND/AGND. As long as you maintain that relationship, regardless of the absolute voltage value, the part will work (just make sure you don't exceed the pin-to-ground maximums, either).