Possible Worlds

Abstract

Recall that the first order modal logic institution MFOL, introduced as an example in Sect. 3.2, refines FOL by adding the modalities of ‘necessity’ and ‘possibility’. While at the sentence level this means a couple of additional unary connectives (□ for ‘necessity” and ⋄ for ‘possibility’), their semantics is much less straightforward because it requires the concept of ‘possible worlds’ semantics, which means that the models are Kripke models, i.e., collections of possible interpretations rather than single interpretation of the signatures. Possible worlds semantics even subtly ‘alters’ the standard semantics of the Boolean connectives and of the quantifiers.