The Expressive Power of the λ-operator and Possibilist Quantifiers in First-order Modal Logics

Abstract

The article presents a comparison of the expressive power of two languages of first-order modal logic: one of them contains the λ-operator and actualist quantifiers, and the other does not contain the λ-operator, but contains actualist quantifiers, possibilist quantifiers and equality. It is shown that there is a truth-preserving translation from the first language to the second one, and that there is no reverse translation. The results show that the second language surpasses the first language in expressive power.