PAULO VITOR MELO VIAL DOMINGUES

Considering the dispute between actualism and possibilism in a model-theoretic framework, we can differ two kinds of quantifiers that, not uncontroversialy, respect the intuitions behind actualism and possibilism: (i) the actualist quantifier whose scope is the domain of the world that the sentence was uttered; (ii) the possibilist quantifier’s scope is the union of the domain of every world. Thus, it is possible to argue that the main difference between actualists and possibilists is the different use of the quantifier: while actualists use the actualist quantifier, possibilists also use the possibilist quantifier. So, the question of the possibility of reducing one discourse on another arises. If w and u are two distinct possible worlds, and the domain of w={a}, u={b}; using the possibilist quantifier we can say that “there is some set that only a and b are members”. However, using only actualists resources (actualists quantifiers and modal operators) we cannot express the sentence above. Thus, our aim is to investigate the possibility of reduction of possibilist discourse.