I've recently come across the Pinocchio Paradox:
If Pinocchio says "my nose will grow."
Does his nose grow or not grow?

Tracing through this scenario, we can see this is related to the Epimenides Paradox.

The scenario in the Pinnochio Paradox assumes Pinnochio can predict when his nose will grow or not grow with perfect accuracy and achieves 100% certainty (an assumption that is a poor representation of real world agentic systems). This is essentially a scenario where Pinnochio has become self-aware that deception causes his nose to grow and has honed his predictive model on what threshold of deception triggers nose growth.

The Pinocchio Paradox is resolved by acknowledging that the word "will" in "will grow " indicates an anticipated future nose growth event; intuitively in the imminent future. The "my nose will grow" message must be in reference to some other action that Pinocchio has taken or a message he transmitted prior to the "my nose will grow" message. When Pinocchio transmits a message, he knows with complete certainty if that message is an act of deception or not. Thus, each message transmission event provides the opportunity for nose growth/non-growth to occur.

Deception exists where there is a difference between Pinnochio's internal model and the model that will be compiled out of the transmitted message upon being received by another agent on the social graph. The difference between 2 models is commonly known as relative entropy or KL Divergence.

For this scenario to work, it also requires an assumption that nose growth lags by at least 2 message passing events, giving room for both the 1st message and 2nd message to be transmitted before nose growth happens. Without this assumption, both Pinocchio and the other agent will have the empirical information of whether Pinocchio's nose grew upon the first event, which would invalidate the purpose of sending the 2nd message that says "my nose will grow."

This also means that we should assume that nose growth happens proportional to the number of deceptive messages transmitted within this trailing 2 message window (else, we wouldn't be able to distinguish the number of messages within this window that contain the deception) Here, nose growth is proportional to the total relative entropy deliberately transmitted within the previous 2 message events.

There are 3 sequential events that occur in this scenario.
Brea...

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