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According to WIkipedia, a notation is a semiotics term to describe artistic disciplines. Famous examples are: chess notation, Siteswap notation for juggling, Labanotation for dancing, basketball play diagrams and the Aresti Catalog (flight maneuvers). In some papers about advanced robotics, also a notation was used to parse motion capture data, for example in the EU Poeticon project lead by Aloimonos, Yiannis. The interesting fact is, that a notation is usually discussed outside of core Artificial Intelligence. It has nothing to do with programming computers itself nor with deeplearning, instead notations are researched by linguists.

They are interesting because they reduce the state space. A notation is some kind of structure to summarize millions of potential states of a system into a handful, which is expressed in a handy grammar. It's not direct an Artificial Intelligence, but it allows to build such a software more easily. In all cases, notations are grounded in natural language, which means that the communication about the topic is done between humans. For example, a basketball team is using a notation for discussing the next move they want to make and they are making signs during the game as a reference.

So my question is: How important are notations for Artificial Intelligence? Can they be used to build robot-control-systems?

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I do not agree that notation is not considered in AI. I think it is very much part of AI, but not necesarily explicitly called "notation".

  1. In robotics

Skill based programming in robotics is a kind of notation, which defines actions. It is a usefull way of defining actions, since it allow a hierarchical approach, define action and (if it has parameters) find optimal paramterset of the action

  1. In classical planning

Notations were the key from the early stages of planning systems, like STRIPS. Actions and states are both defined symbolically, so this is a kind of notation. This notation allows the problem to be defined in a STRIPS framework.

  1. In reinforcement learning

Any kind of reduction in state/action space, any kind of descretization or lattice space definition based on expert knowledge is in fact a kind of notation, which contributes to reduction of the problem complexity.

  1. In (un)supervised learning

Principal component analysis can be used to determine the independent parameter space and reduces the problem dimention. In this sence it defines a new notation, simpler then the original one.

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