 Dual-domain semantics have been criticized as ontologically extravagant. In response, some authors have advocated single-domain positive semantics, which assign no denotation to empty singular terms. In such semantics empty-termed atomic formulas require unconventional treatment. Typically such semantics determine the truth-values of atomic formulas in two different ways: a Tarksi-style calculation for formulas whose terms all refer, and a separate truth-value assignment for empty-termed atomic formulas. The details, however, tend to get complicated. Antonelli (2000), for example, advocated such a single-domain free logic, which he called proto-semantics, but more recently (2007, p. 72) he has characterized all semantics for positive free logic as “somewhat artificial” and has questioned the logical character of free quantification in general.