A question about logic. When symbolizing and making inferences in natural languages that contain such terms as "it is necessary that", "A ought to do X", "A knows X", and "it is always the case that", there are extensions of classical logic, respectively, modal, deontic, epistemic, and tense logic that attempt to deal with such natural language analogues.
My question is: What about propositions that contain a mixture of all the above terms? For example, there are sentences in natural language of the form “It is necessary that John ought to always know that 2+2=4." Is there a logic that can effectively handle (i.e. symbolize and correctly infer) such propositions? If so, is this logic both sound and complete? If there is no such logic, what is a logician to do with such propositions?
My intuition is that things get tricky when you mix these operators together and/or the classical quantifiers.
Thanks kindly for your reply,
A Concerned Thinker