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 commonly said ... that ridicule is the best test of truth; for that it will not stick where it is not just. I deny it. A truth learned in a certain light, and attacked in certain words, by men of wit and humour, may, and often doth, become ridiculous, at least so far, that the truth is only remembered and repeated for the sake of the ridicule.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“The test of a real comedian is whether you laugh at him before he opens his mouth.”
—George Jean Nathan (1882–1958)
“I am willing, for a money consideration, to test this physical strength, this nervous force, and muscular power with which I’ve been gifted, to show that they will bear a certain strain. If I break down, if my brain gives way under want of sleep, my heart ceases to respond to the calls made on my circulatory system, or the surcharged veins of my extremities burst—if, in short, I fall helpless, or it may be, dead on the track, then I lose my money.”
—Ada Anderson (1860–?)