XL's many-sorted quantification over heterogeneous domains may generate validity-preservation failures under certain sort-collapsing interpretations that standard enumeration procedures miss.

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Heterogeneous domains(in logic): Different groups or sets of things that are unlike each other—for example, numbers and colors would be heterogeneous because they're fundamentally different kinds of things.
Many-sorted quantification(in logic and mathematics): A logical system that counts or measures over different types or categories of things separately, rather than treating everything the same way.
Sort-collapsing interpretations(in logic): Ways of reading or understanding a logical system where you treat different types of things as if they were the same type, merging categories that should stay separate.
Standard enumeration procedures(in logic and mathematics): The usual or common methods for listing out and checking all the cases or possibilities in a logical system.
Validity-preservation(in logic and reasoning): When a logical argument stays true and correct even when you apply it in different situations or change how you interpret it.
XL(as a formal system in logic): A specific formal logical system (a set of rules and symbols for expressing ideas precisely); the letters refer to a particular version of logic, likely one that extends standard logic in some way.

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