Dynamic Logic (modal Logic) - Language

Language

Modal logic is characterized by the modal operators (box p) asserting that is necessarily the case, and (diamond p) asserting that is possibly the case. Dynamic logic extends this by associating to every action the modal operators and, thereby making it a multimodal logic. The meaning of is that after performing action it is necessarily the case that holds, that is, must bring about . The meaning of is that after performing it is possible that holds, that is, might bring about . These operators are related by and, analogously to the relationship between the universal and existential quantifiers.

Dynamic logic permits compound actions built up from smaller actions. While the basic control operators of any programming language could be used for this purpose, Kleene's regular expression operators are a good match to modal logic. Given actions and, the compound action, choice, also written or, is performed by performing one of or . The compound action, sequence, is performed by performing first and then . The compound action, iteration, is performed by performing zero or more times, sequentially. The constant action or BLOCK does nothing and does not terminate, whereas the constant action or SKIP or NOP, definable as, does nothing but does terminate.