Test
Dynamic logic associates to every proposition an action called a test. When holds, the test acts as a NOP, changing nothing while allowing the action to move on. When is false, acts as BLOCK. Tests can be axiomatized as follows.
A8.
The corresponding theorem for is:
T8.
The construct if p then a else b is realized in dynamic logic as . This action expresses a guarded choice: if holds then is equivalent to, whereas is equivalent to BLOCK, and is equivalent to . Hence when is true the performer of the action can only take the left branch, and when is false the right.
The construct while p do a is realized as . This performs zero or more times and then performs . As long as remains true, the at the end blocks the performer from terminating the iteration prematurely, but as soon as it becomes false, further iterations of the body are blocked and the performer then has no choice but to exit via the test .
Read more about this topic: Dynamic Logic (modal Logic)
Famous quotes containing the word test:
“The test of a vocation is the love of the drudgery it involves.”
—Logan Pearsall Smith (1865–1946)
“Poetry is important. No less than science, it seeks a hold upon reality, and the closeness of its approach is the test of its success.”
—Babette Deutsch (1895–1982)
“There is a parallel between the twos and the tens. Tens are trying to test their abilities again, sizing up and experimenting to discover how to fit in. They don’t mean everything they do and say. They are just testing. . . . Take a good deal of your daughter’s behavior with a grain of salt. Try to handle the really outrageous as matter-of-factly as you would a mistake in grammar or spelling.”
—Stella Chess (20th century)