Hello,
I also see an oscillator strongly connected to positive or "regenerative" feedback. Proceeding from oszillators, that have an amplifier as recognizable building block, e. g. a typical crystal oszillator, you can define a simple oscillator condition: The loop gain for the oscillation frequency must be +1. Different formula signs are usual for the parameters, e. g. A•β = 1. A is the amplifier gain, β is the feedback in this formula, the relation applies to the vectorial quantities.
It's not said, if the resonant element is contained in the A or the β term. Furthermore if A has negative sign, β would be negative too. You could call this an oscillator with negative feedback, but not in the usual meaning. Steady state is provided for this consideration. Otherwise, oscillation amplitude would either decrease and quickly die down or increase and reach steady state at the amplifier's apmplitude limits.
Non-steady state phenomena, e. g. cyclic oszillations can't be described by simple linear circuit theory, therefore the term feedback looses it's unequivocal meaning in this connection. You can find theoretical descriptions of such phenomena in nonlinear control theory as well as in chaos theory.
Regards,
Frank