additive abstractions and bookkeeping
Okay, additive abstractions are used in artificial intelligence, particularly puzzle solving.
An abstraction is an easier version of a puzzle. Imagine a Rubik's cube with every side grey - how easy would it be to solve? Very easy - zero moves. What about a cube with one side blue and the rest grey? Easier than the cube as a whole.
If you can easily solve the abstracted puzzle, you can use the length of the solution to the abstracted puzzle as a heuristic. If you can see that the abstraction will take at least 4 moves to solve, and then the whole puzzle will also take at least 4 moves to solve.
The usual way to combine abstractions is to be conservative - if one way of looking at it guarantees that it will take 4, and another way promises it will take at least 10, then use 10 as the heuristic distance to the goal, and you won't be wrong. Additive abstractions are especially "orthogonal" to each other, so that you can take the sum, rather than the max. For example, in the 15-puzzle, the number of moves to get the 1 and 2 to the right positions is a non-additive abstraction. The number of moves, counting only the moves that actually do move the 1 or the 2 (but counting the motion of the grey squares as free) is an additive abstraction.
In bookkeeping, you set up accounts for things like "the contents of warehouse 3" or "the amount of gold that I have stored in all of my warehouses". Those accounts are additive abstractions of your entire business. This analogy points out a concrete and specific way that businesses are varieties of artificial intelligence (and have been at least since Pacioli documented the existing-at-that-time accounting practices in 1494).
This analogy also suggests it might be valuable to port specific ideas from one domain to the other: Would it be helpful to log all of the additions and subtractions to each component of an additive heuristic, as the agent solves the problem, and try to compress it and therefore learn to anticipate? Would it be helpful (perhaps it's already common) to use max abstractions in bookkeeping; do the books looking at the world through several different lenses, and report only the most conservative one for decision-making purposes?
An abstraction is an easier version of a puzzle. Imagine a Rubik's cube with every side grey - how easy would it be to solve? Very easy - zero moves. What about a cube with one side blue and the rest grey? Easier than the cube as a whole.
If you can easily solve the abstracted puzzle, you can use the length of the solution to the abstracted puzzle as a heuristic. If you can see that the abstraction will take at least 4 moves to solve, and then the whole puzzle will also take at least 4 moves to solve.
The usual way to combine abstractions is to be conservative - if one way of looking at it guarantees that it will take 4, and another way promises it will take at least 10, then use 10 as the heuristic distance to the goal, and you won't be wrong. Additive abstractions are especially "orthogonal" to each other, so that you can take the sum, rather than the max. For example, in the 15-puzzle, the number of moves to get the 1 and 2 to the right positions is a non-additive abstraction. The number of moves, counting only the moves that actually do move the 1 or the 2 (but counting the motion of the grey squares as free) is an additive abstraction.
In bookkeeping, you set up accounts for things like "the contents of warehouse 3" or "the amount of gold that I have stored in all of my warehouses". Those accounts are additive abstractions of your entire business. This analogy points out a concrete and specific way that businesses are varieties of artificial intelligence (and have been at least since Pacioli documented the existing-at-that-time accounting practices in 1494).
This analogy also suggests it might be valuable to port specific ideas from one domain to the other: Would it be helpful to log all of the additions and subtractions to each component of an additive heuristic, as the agent solves the problem, and try to compress it and therefore learn to anticipate? Would it be helpful (perhaps it's already common) to use max abstractions in bookkeeping; do the books looking at the world through several different lenses, and report only the most conservative one for decision-making purposes?