We propose a logical framework to analyze complex predicates (those involving a subquery) in SQL. We propose a new operator in the relational algebra for handling such predicates, and study its properties and how it combines with traditional relational operator. We focus on predicates of the form att θ MOD S, where att is an attribute, θ a comparison operator, MOD is one of SOME or ALL, and S is a (correlated or non-correlated) subquery. We provide a formal characterization of these predicate, as well as an implementation and optimization strategies for it. We show that our approach is extendible, so we can support the expression and optimization of other, similar predicates. Finally, we describe experimental evidence that the proposed approach is more efficient than the traditional approach across a variety of conditions.