>[!abstract] >Lossy implications happen when inferential steps lose some informational content — e.g., from stronger to weaker statements, as is common in non-classical logic or probabilistic reasoning. For example: while $(A = B \land B = C) \implies (A = C)$ is true in a formal sense, $(A \approx B \land B \approx C) \implies (A \approx C)$ is not. The cumulative approximations may nearly cancel each other out, or they may compound — there is no way to tell just from those statements. >[!quote] >While following logical threads to their conclusions is a useful exercise, each logical step often involves some degree of rounding or unknown-unknowns. A -> B and B -> C means A -> C in a formal sense, but A -almostcertainly-> B and B -almostcertainly-> C does not mean A -almostcertainly-> C. Rationalists, by tending to overly formalist approaches, tend to lose the thread of the messiness of the real world and follow these lossy implications as though they are lossless. ([[rachofsunshine, 2025]]). >[!related] >- **North** (upstream): [[Non-classical logic]] >- **West** (similar): [[Intransitivity]], [[Non-monotonic reasoning]] >- **East** (different): [[Truth-preserving inference]] (classical entailment) >- **South** (downstream): [[Probabilistic entailment]]