When I studied chemical engineering I often found the need to rewrite lecture notes, handouts and books in order to gain a thorough understanding of the subject I was reading. As much as time permitted I used to draw mindmaps of the reading material combining the symbols on the left in the image below:
The first ones are probably known, but some of these may need some explanation. I will list all of them with my own explantions to make clear what I mean.
- B is a part of A. B is a subset of A. B is a property of A.
- B is partly a part of A. B is a almost a subset of A. B is to a very small degree a property of A.
- A equals B. A and B are the same thing.
- B is a consequence of A. If A happens then B happens as a consequence.
- A becomes B. First there is only A, later there is only B.
- This describes a process or a verb. A is put into B. Example: A reactant (A) is fed into a reactor (B).
- A affects property B and causes a decrease, and B is a property of some other object as drawn in 1.
- A affects property B and causes an increase, and B is a property of some other object as drawn in 1.
- A intends to cause B to come into existance. Example: A company (A) strives to create profit (B).
- A strives/wants/intends to become B. Example: One strives to keep the concentration of reactant (A) in a reactor to be 0.1 mol/liter (B).
What are the conventional mathematical names and symbols used to denote these relations above?
Edit 19.5.2013: Just as an example I analyzed a sentence taken from a paper by Ernest Davis about technological singularity:
It is not perfect though.