Extending Kamp's Theorem to Model Time Granularity

In this paper, a generalization of Kamp's theorem relative to the functional completeness of the until operator is proved. Such a generalization consists in showing the functional completeness of more expressive temporal operators with respect to the extension of the first‐order theory of linear orders MFO[<] with an extra binary relational symbol. The result is motivated by the search of a modal language capable of expressing properties and operators suitable to model time granularity in ω‐layered temporal structures.