Logic & Philosophy of Science Colloquium

In standard modal the Box is a sentential operator. Consequently, necessity, and other modal, deontic, temporal etc. notions are formalized as operators of sentences. This means that quantified sentences as "All axioms of PA are necessary" cannot be formalized in a straightforward way. Thus it is desirable to formalize these intentional notions as predicates of sentences or propositions. Possible worlds semantics for sentential operators can be provided in a straightforward way. As Kamp, Gupta and others have shown, possible worlds semantics is also feasible to some extent, if necessity etc. are conceived as predicates of sentences. While models may be based on arbitrary frames of the operator view, models cannot be based on certain frames of the predicate view. Possible worlds semantics for predicates excludes certain classes of frames, e.g., reflexive frames, while others, e.g., converse wellfounded frames admit suitable models. The restrictions follow from the paradoxes of modality (e.g., Montague's paradox). We investigate the following problem: On which frames can one build possible-worlds models for predicates of sentences?