 Cocchiarella’s ideas have been presented in more rigorous formal detail with axioms and consistency and completeness results for second-order logic in Freund (2000), tense logic (2001) and modalities (2004). More recently, Freund (2019) has formulated several bidimensional logics for sortals that consider modal, tense, and epistemic modalities, as well as complex sortals (i.e., sortals that involve logical combinations of other sortals). These systems presuppose a conceptualist philosophical background closely related to Cocchiarella’s but somewhat more general.