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Equation 1 · Part 3 · Typed Tools: Protocols as an Agent's Action Alphabet

Symbol Sigma

t: At×Σ  ⇀  Rt×Σt:\ \mathcal{A}_t \times \Sigma \;\rightharpoonup\; \mathcal{R}_t \times \Sigma
Σ\Sigma

What this part means

Sigma is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

Sigma is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

Start with the smallest honest model. A tool is not a function in the mathematical sense, because it touches the world. Write it as a partial map from arguments and world-state to results and world-state: t: At×Σ  ⇀  Rt×Σt:\ \mathcal{A}_t \times \Sigma \;\rightharpoonup\; \mathcal{R}_t \times \Sigma. Four things are named there, and each corresponds to a design decision that is usually made by accident.

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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