Oswald, James T.Rozek, BrandonFerguson, Thomas M.2024-11-182024-11-1820241610-1987http://dx.doi.org/10.1007/s13218-024-00848-7https://dl.gi.de/handle/20.500.12116/45390We introduce the $$\mathscr {C}^{0}$$ C 0 family of logics, which include temporalized modal operators for belief and hyperintensional modal operators for obligations and goals. We motivate the $$\mathscr {C}^{0}$$ C 0 family as extended doxastic fragments of the $$\mathcal {DCEC}$$ DCEC family of logics, which are cognitive calculi designed for theory-of-mind reasoning among multiple artificial agents. In the literature, $$\mathcal {DCEC}$$ DCEC family logics are defined exclusively using proof-theoretic semantics. In this work we provide a model theory for the $$\mathscr {C}^{0}$$ C 0 family of logics which constitutes the first steps towards providing a model theory for the $$\mathcal {DCEC}$$ DCEC cognitive calculi family as a whole. We investigate the fragment relationships between both the $$\mathscr {C}^{0}$$ C 0 family and the $$\mathcal {DCEC}$$ DCEC family, produce a model theory for the $$\mathscr {C}^{0}$$ C 0 family and prove important results establishing completeness for all $$\mathscr {C}^{0}$$ C 0 family logics and establish soundness for $$\mathscr {C}^{0}$$ C 0 fragments without time.Text/Journal Article10.1007/s13218-024-00848-7