Monoidal Logics: How to Avoid Paradoxes

Monoidal logics are logics that can be seen as specific instances of monoidal categories. They are constructed using specific rules and axiom schemata that allow to make explicit the monoidal structure of the logics. Among monoidal logics, we find Cartesian logics, which are instances of Cartesian categories. As it happens, many paradoxes in epistemic, deontic and action logics can be related to the Cartesian structure of the logics that are used. While in epistemic and deontic logics the source of the paradoxes is often found within the principles that govern the modal operators, our framework enables us to show that many problems can be avoided by adopting a proper monoidal structure. Thus, the usual modal rules and axiom schemata do not necessarily need to be discarded to avoid the paradoxes. In this respect, monoidal logics o↵er an alternative way to model knowledge, actions and normative reasoning. Furthermore, it provides us with new avenues to analyze modalities.