A Norm-based Truthmaker Semantics for Modal Logic

Abstract In the last few decades, truthmaker semantics has attracted the attention of scholars from various areas, arguably due to its philosophical underpinning and its flexibility in addressing a number of problems that are difficult to solve using alternative semantic frameworks. Attention is now focused on developing truthmaker semantics for modal logic; this paper contributes to that direction. The basic idea we introduce is that truthmakers of modal sentences are norms. This allows us to derive two interesting results: first, we introduce a new modal semantics for minimal monotonic logic; second, we provide a truthmaker semantics for every modal logic characterized by a class of Kripke frames. This is, as far as we can tell, the first general result about truthmaker semantics for normal modal logics.