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 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)
“There is held to be no surer test of civilisation than the increase per head of the consumption of alcohol and tobacco. Yet alcohol and tobacco are recognisable poisons, so that their consumption has only to be carried far enough to destroy civilisation altogether.”
—Havelock Ellis (1859–1939)