Ask A Genius 1445: Default and Autoepistemic Logic: Bayesian Reasoning and Self-Referential AI
Author(s): Rick Rosner and Scott Douglas Jacobsen
Publication (Outlet/Website): Ask A Genius
Publication Date (yyyy/mm/dd): 2025/07/11
Scott Douglas Jacobsen and Rick Rosner examine default logic, Bayesian inference, and autoepistemic logic in artificial intelligence. They compare default assumptions to scientific experimentation, illustrate Bayesian updates through real-world examples like ID checking, and explore recursive belief models where agents form and revise beliefs about their own reasoning processes.
Scott Douglas Jacobsen: I was thinking in one-bit logic, but it is not relevant here. So—default logic. It allows reasoning with default assumptions unless those assumptions are contradicted. You assume a baseline, reason forward using “if-then” structures, but you always refer back to that baseline. If your result contradicts the default, then you drop the assumption or shift the reasoning. It is basically how you would run a scientific experiment.
You assume certain premises, then you run the experiment based on those. If the results contradict your assumptions, you throw them out. Alternatively, update the model.
Rosner: That sounds Bayesian. Bayesian reasoning is a formal way of saying: you start with a set of initial assumptions, and then you allow new data—further experience—to act on those assumptions. Either reinforcing them or sending them packing.
Your assumptions are called priors—your starting beliefs before encountering new data or evidence.
Jacobsen: And you can weigh those priors, right? Depending on how confident you are in them to begin with.
Rosner: Exactly. Let us go back to something experiential, like being a bouncer checking IDs. I checked hundreds of thousands of IDs in bars. Eventually, I got good at it. I had strong priors that I would apply to every new dataset, which was each person walking up and handing me an ID.
My previous experience had a high degree of influence on how I judged someone initially, whether I thought they were lying or not. Then, as I gathered more evidence—how they acted, how their signature looked, how they answered questions—I updated my conclusion accordingly.
So yes, that’s default logic in action. However, it is also Bayesian. What is next?
Jacobsen: Autoepistemic logic. It models an agent’s beliefs about its own beliefs. We briefly discussed this last time, but ran out of time or lost the thread—self-referential epistemic logic. The agent not only holds beliefs but also forms beliefs about those beliefs. It is a belief recursion—a belief about belief.
However, there is something weird in how it is formalized, because technically, a model is encoded in a structure—it is not conscious. So it is like calling it a meta-model, but without actual subjectivity. Still, the model behaves as if it has subjectivity.
Moreover, that loops right back into how thought works. When you think, you are thinking about thinking. Thought is recursive. You are constantly running your assumptions through different analytic modules in your mind, trying—at least in the moment—to build a consistent picture of reality.
Jacobsen: So, yes, what you are doing there is testing your logic.
Rosner: New instances of your logic are tested against the logic itself. Fine.
Jacobsen: Yes. That is it.
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