I like the notation of "product across X" for "for all". I don't intuit the "sum across x" for "there exists", that seems more distinct. Although I can see that

I like the notation of "product across X" for "for all". I don't intuit the "sum across x" for "there exists", that seems more distinct. Although I can see that applying OR of the predicate across the population would achieve the same result. It would be nice to express logical aggregations such as AND and OR across sets like sum and product can be. Since their symbols are not Greek letters, it's not as simple as choosing the capitalized letter. For that matter, a way of separating map-reduce from the reduction function, so that max, min, or other functions can be expressed uniformly, would also seem like an advancement. Probably it's been done and I'm simply ignorant.