Modal logic

This paper surveys the main concepts and systems of modal logic. It shows how the tree or tableau method provides a simple and easily comprehensible decision procedure for systems such as K, T, S4 and S5. It also shows how the formal techniques of modal logic can be used to analyse several informal problems involving modal concepts, including cases combining modality with quantification. Although much as the discussion is in terms of the possible worlds interpretation of the modalities, provability interpretations are also examined. One of the central applications of modal operators within Artificial Intelligence (AI) is then discussed: the analysis of non-monotonic reasoning.