A multimodal logic is a modal logic that has more than one primitive modal operator.
They find substantial applications in theoretical computer science.
, to give a classical multimodal logic if it is in addition stable under necessitation (or "possibilization", therefore) of both members of provable equivalences.
Perhaps the first substantive example of a two-modal logic is Arthur Prior's tense logic, with two modalities, F and P, corresponding to "sometime in the future" and "sometime in the past".
A logic[1] with infinitely many modalities is dynamic logic, introduced by Vaughan Pratt in 1976 and having a separate modal operator for every regular expression.
A version of temporal logic introduced in 1977 and intended for program verification has two modalities, corresponding to dynamic logic's [A] and [A*] modalities for a single program A, understood as the whole universe taking one step forwards in time.
The term multimodal logic itself was not introduced until 1980.
Multimodal logic can be used also to formalize a kind of knowledge representation: the motivation of epistemic logic is allowing several agents (they are regarded as subjects capable of forming beliefs, knowledge); and managing the belief or knowledge of each agent, so that epistemic assertions can be formed about them.
must be capable of bookkeeping the cognition of each agent, thus
For formalization of meaning based on the possible world semantics approach, a multimodal generalization of Kripke semantics can be used: instead of a single "common" accessibility relation, there is a series of them indexed on the set of agents.