Free logic, not an enriched first-order predicate, is the proper formal tool for handling non-referring terms like 'dragon', preserving a neutral domain without inflating the predicate inventory.
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domain(Both f1 and f2 have the reals as their domain)
The set of input values over which a function is defined.
free logic(Contrasted with standard first-order predicate logic)
A logical system in which the existential generalization '∃x φ(x)' cannot in general be derived from 'φ(t)' for a singular term 't', meaning singular terms do not automatically carry existential import