What is the conventional notation for these logic statements?

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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.

  1. B is a part of A. B is a subset of A. B is a property of A.
  2. 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.
  3. A equals B. A and B are the same thing.
  4. B is a consequence of A. If A happens then B happens as a consequence.
  5. A becomes B. First there is only A, later there is only B.
  6. This describes a process or a verb. A is put into B. Example: A reactant (A) is fed into a reactor (B).
  7. A affects property B and causes a decrease, and B is a property of some other object as drawn in 1.
  8. A affects property B and causes an increase, and B is a property of some other object as drawn in 1.
  9. A intends to cause B to come into existance. Example: A company (A) strives to create profit (B).
  10. 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?

Answer

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