Aristotalian logic was what was under discussion. I know it supports two operators because that's all I use when do traditional sorite(s).
The IMPLYs operator, as I've now demonstrated several times to Tares, applies between the major and minor predicates to produce a new statement. The NOT operator can be applied to a predicate. This is embodied in the various patterns you memorized that make up the valid implications of Aristotalian logic. All these are, is the IMPLYs operator for every combination of of universal and existential implication that's valid between two predicates.
The reason I know it, is that there ain't anything else to Aristotalian logic. Hard as you look, you will not find an AND or OR or NOR operator in use as a machine to derive predicates. You will only find them absorbed inside a predicate, where their logical function is irrelevant. The way to test this, as I have been trying convince tares, is to substitute a meaningless word for anything you think is logic inside a predicate, and see if you can still work the problem.
Can the boolean operator IMPLY be derived from the Aristotalian operator IMPLY if I treat the Aristotalian predicates as boolean objects?