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.
Read more about this topic: Dynamic Logic (modal Logic)
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Famous quotes containing the word language:
“We have tried so hard to adulterate our hearts, and have so greatly abused the microscope to study the hideous excrescences and shameful warts which cover them and which we take pleasure in magnifying, that it is impossible for us to speak the language of other men.”
—Charles Baudelaire (18211867)
“Philosophy is written in this grand bookI mean the universe
which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it.”
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“Because language is the carrier of ideas, it is easy to believe that it should be very little else than such a carrier.”
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