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:
“It is the test of a novel writer’s art that he conceal his snake-in-the-grass; but the reader may be sure that it is always there.”
—Anthony Trollope (1815–1882)
“A test of what is real is that it is hard and rough. Joys are found in it, not pleasure. What is pleasant belongs to dreams.”
—Simone Weil (1909–1943)
“The test of an adventure is that when you’re in the middle of it, you say to yourself, “Oh, now I’ve got myself into an awful mess; I wish I were sitting quietly at home.” And the sign that something’s wrong with you is when you sit quietly at home wishing you were out having lots of adventure.”
—Thornton Wilder (1897–1975)