Modal Logic is any system of formal logic that attempts to deal with modalities (expressions associated with notions of possibility, probability and necessity). Modal Logic, therefore, deals with terms such as "eventually", "formerly", "possibly", "can", "could", "might", "may", "must", etc.
Modalities are ways in which propositions can be true or false. Types of modality include:
Alethic Modalities: Includes possibility and necessity, as well as impossibility and contingency. Some propositions are impossible (necessarily false), whereas others are contingent (both possibly true and possibly false).
Temporal Modalities: Historical and future truth or falsity. Some propositions were true/false in the past and others will be true/false in the future.
Deontic Modalities: Obligation and permissibility. Some propositions ought to be true/false, while others are permissible.
Epistemic Modalities: Knowledge and belief. Some propositions are known to be true/false, and others are believed to be true/false.
Although Aristotle's logic is almost entirely concerned with categorical syllogisms, he did anticipate modal logic to some extent, and its connection with potentiality and time. Modern modal logic was founded by Gottlob Frege, although he initially doubted its viability, and it was only later developed by Rudolph Carnap (1891 - 1970), Kurt Gödel (1906 - 1978), C.I. Lewis (1883 - 1964) and then Saul Kripke (1940 - ) who established System K, the form of Modal Logic that most scholars use today).