What Is A Question?

This post is based on my article at https://arxiv.org/abs/1006.2481. References therein.

According to Richard T. Cox, a question is the set of assertions that answer it. Following R.T. Cox, we identify a question with a topology on a given set of irreducible assertions. It appears that a question is expressed in the form of multiple choices. Here is an example

Q1: What is a particle?

A. A particle has mass.

B. A particle has spin.

C. A particle has mass and spin.

D. None of the above.

In the sense of topology, the ground set is {mass, spin}. The topology is {{}, {mass}, {spin}, {mass, spin}}. The members of a topology are called open sets.

In other words, these are investigative questions that rule out less probable issues. To further elaborate add charge in the above example,

Suppose mass = m, spin = s, and charge = e. The ground set would be X= {m, s, e}, and the topology

T = {{}, {m}, {m, s}, {m, e}, {m, s, e}}

One gets different results based on what is ruled out. When mass is ruled one gets

T0= {{}}

BY eliminating spin, one has

T1 = {{}, {m},{m,e}}

and the elimination of charge gives

T2 = {{}, {m}, {m, s} }

We can also define a negation question. Let T be a question. Since the elements of T are open sets, we can define a collection of closed sets. In the above example, we had

TC= {{}, {s,e}, {e}, {s}, {m, s, e}}

One can see there are elements that are both in T and TC. These elements are called clopen sets.

Questions are very important in machine learning. A machine asks the question, T. For every machine, there is an anti-machine that asks negation question TC. A machine and an anti-machine make a universe. Generally, a universe consists of a system and environment. The system and environment communicate through clopen sets.

In conclusion we suggest that an intelligent communicates with the user in the through of dialogues.