Does this theory to what extend it holds essentially true

Hi team,

Do you think, this below theory to what extent holds true.

When Stock increases , OI increases.(bullish)

When Stock Decreases, OI increases leading to short selling.

When Stock Decrease, OI decrease leading to short covering.

When Stock Increase, OI decrease leading to profit booking (in the context of options trade)

The theory is that 

  • Stock increases with increase in OI, that means it is more bullish. 
  • Stock increases with decrease in OI, that means it is not really fresh longs coming in but existing shorts covering. So not as bullish as the first scenario. 
  • Stock decreases with increase  in OI, that means it is more bearish as fresh shorts coming in. 
  • Stock decreases with decrease in OI, that means it is not fresh shorts coming in but the existing longs covering. So not as bearish as the above scenario. 
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I believe that for the discussion on OI(derivative concept), the underlying stock future has to be considered and not the stock(cash market). For relation between OI and the underlying derivative, pls refer the answer for a similar query

Live Eg: Currently Bharti Airtel call option 400 OI is increasing daily since the Day 1 of Dec expiry, however stock is going down, so here your 3rd point comes into picture, Am i correct?

Yep, that could mean so.