 Optimality Theory (OT) is a linguistic theory which assumes that linguistic choices are governed by competition between a set of candidates, or alternatives. In standard OT (Prince &amp; Smolensky, 1993) the optimal candidate is the one that satisfies best a set of violable constraints. After its success in phonology, OT has also been used in syntax, semantics and pragmatics. The original idea of optimality-theoretic semantics was to model interpretation by taking the candidates to be the alternative interpretations that the hearer could assign to a given expression, with constraints describing general preferences over expression-interpretation pairs. Blutner (1998, 2000) extended this original version by taking also alternative expressions, or forms, into account that the speaker could have used, but did not. The reference to alternative expressions/forms is standard in pragmatics to account for Quantity implicatures. Optimization should thus be thought of from two directions: that of the hearer, and that of the speaker. What is optimal, according to Blutner’s Bidirectional-OT (Bi-OT), is not just interpretations with respect to forms, but rather form-interpretation pairs. In terms of a ‘better than’ relation ‘\(\gt\)’ between form-interpretation pairs, the pair \(\langle f,i\rangle\) is said to be (strongly) optimal iff it satisfies the following two conditions: