[Artificial intelligence] shutdown problem, Russell Paradox and three-valued logic

1. Russell Paradox

There is a collection of A={x|x∉a}. So the question is: does a belong to a?

Equivalent to the popular saying "Barber paradox": The Barber said only to the city do not give their heads head, and then every day to find his head of the endless stream of people, one day, the question came: the Barber to his head?

The key to the Russell paradox lies in the definition of its own invocation .

2, halting problem (stop problem)

There is a program, its input is a program and its parameters, the output is to determine whether the input program will be down.

The shutdown problem can be proved to be pseudo-proposition.

In order to prove that this shutdown judgment program does not exist, use contradiction:

Reference: http://blog.csdn.net/niushuai666/article/details/7260957

Suppose there is an outage judgment procedure

BOOL God_algo (charChar* input) {    if(<program> halts on <input>)         return true ;     return false ;}

There's another reverse procedure.

BOOL Satan_algo (Char* program ) {if(God_algo. Program)}       {while (1);        // Loop forever!       return false;   // can never get here! }else       returntrue;}

Then when it calls itself, the Satan_algo (SATAN_ALGO) program will not be able to determine the output result.

3, three-value logic

The key point of the Russell paradox and the downtime problem is that there will be an ambiguous state when invoking itself.

The logical flaw in both is that it adheres to the two-value logic, which means that things are not real or false : The Barber finds himself doing only two things, either cutting his head or not cutting his head. The final output of all programs in the outage problem is only two states, either down or without downtime. But the real world is not two-valued, like Schrödinger's cat, there is a middle state. So the world needs three-valued logic.

The three-valued logic holds that if 1 is true and 0 is false, then there is a state 1/2 that is not true or false, and also true and false.

The third Truth 1/2 is interpreted as the Russell paradox, "all collections that do not consist of elements of itself are itself", and in turn "all collections that do not set themselves as elements do not belong to itself" is also 1/2

That is (*) P↔"p is True

[Artificial intelligence] shutdown problem, Russell Paradox and three-valued logic