Modal logic systems are extensions of classical logic that introduce modalities, which express concepts like necessity and possibility. In these systems, statements can be evaluated not just as true or false, but also in terms of whether they are necessarily true, possibly true, or contingently true. This allows for more nuanced reasoning about propositions. There are various modal logic systems, such as K, S4, and S5, each with different axioms and rules governing the modalities. These systems are used in various fields, including philosophy, computer science, and linguistics, to analyze and formalize reasoning about knowledge, belief, and time.