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:
“I have come to believe ... that the stage may do more than teach, that much of our current moral instruction will not endure the test of being cast into a lifelike mold, and when presented in dramatic form will reveal itself as platitudinous and effete. That which may have sounded like righteous teaching when it was remote and wordy will be challenged afresh when it is obliged to simulate life itself.”
—Jane Addams (1860–1935)
“The test of a given phrase would be: Is it worthy to be immortal? To “make a beeline” for something. That’s worthy of being immortal and is immortal in English idiom. “I guess I’ll split” is not going to be immortal and is excludable, therefore excluded.”
—Robert Fitzgerald (1910–1985)
“To test a modest man’s modesty do not investigate if he ignores applause, find out if he abides criticism.”
—Franz Grillparzer (1791–1872)