(Disclaimer: This post was written as part of the CFAR/MIRI AI Summer Fellows Program, and as a result is a vocalisation of my own thought process rather than a concrete or novel proposal. However, it is an area of research I shall be pursuing in the coming months, and so ought to lead to the germination of more ideas later down the line. Credit goes to Abram Demski for inspiring this particular post, and to Scott Garrabrant for encouraging the AISFP participants to actually post something.)

When reading Soares' and Levinstein's recent publication on decision theory, Death in Damascus, I was struck by one particular remark:

Unfortunately for us, there is as yet no full theory of counterlogicals [...], and for [functional decision theory (FDT)] to be successful, a more worked out theory is necessary, unless some other specification is forthcoming.

For some background: an FDT agent must consider counterfactuals about what would happen if its decision algorithm on a given input were to output a particular action. If the algorithm is deterministic (or the action under consideration is merely outside of the range of possible outputs of the agent), then it is a logical impossibility that the algorithm produces a different output. Hence the initial relevance of logical counterfactuals or counterlogicals: counterfactuals whose antecedents represent a logical impossibility.

My immediate thought about how to tackle the problem of finding a full theory of counterlogicals was to find the right logical system that captures counterlogical inference in a way adequate to our demands. For example, Soares and Fallenstein show in Toward Idealized Decision Theory that the principle of explosion (from a contradiction, anything can be proved) leads to problematic results for an FDT solution. Why not simply posit that our decision theory uses paraconsistent logic in order to block some inferences?

Instead, and to my surprise, Soares and Levinstein appear to be more concerned about finding a semantics for logical counterfactuals - loosely speaking, they are looking for a uniform interpretation of such statements which shows us what they really mean. This is what I infer from reading the papers it references on theories of counterlogicals such as Bjerring's Counterpossibles, which tries to extend Lewis' possible-worlds semantics for counterfactuals to cases of logical

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