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Published equation contexts

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

Why this formula appears here

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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tt

Symbol t

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Σ\Sigma

Symbol Sigma

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

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Published contexts (1)

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

Equation 1 · AI Agents & Systems

Typed Tools: Protocols as an Agent's Action Alphabet

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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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