Logical Inference

Logical inference is a deterministic derivation: given stated premises, the conclusion follows necessarily. It is not an L0 atom. L0 is where regress terminates — a committed decision or a designated observation. Inference starts from L0 (or lower-uncertainty artifacts) and produces something at least one processing step away: typically L1 for a single deductive step with explicit causal references (a balance from transactions, a tier-2 restatement with cited premises), or L2 when multiple steps, streams, or rule chains sit between premises and conclusion.

The conclusion generalizes above the concrete L0 facts: a rule fires, a sum collapses many events, a universal is inferred from witnesses. Unless the artifact bijectively encodes every premise (rare, and then it is barely inference — mostly packaging), the output forgets which specific L0 instances supported it. You cannot recover the full transaction history from the balance; you cannot recover every cited passage from “therefore approved” without the citation contract. That is information loss relative to ground truth even when the step is deductively valid and probabilistically lossless (η = 1 for the stochastic component — same premises always yield the same conclusion).

Formally: in a Markov chain from concrete L0 set X through inference Y to generalized conclusion Z, the data processing inequality gives I(X ; Z) ≤ I(X ; Y); strict inequality holds whenever the map is not invertible — which is the normal case for generalization. Atomicity and mutual-information loss are therefore independent of probabilistic η.

Committing to an inferred conclusion at a commitment boundary does not promote the inference to L0. The decision to adopt the conclusion may be L0; the derived statement remains L1 or L2 with an explicit chain back to premises.

At the commitment boundary

Where the answer is deterministic and feasible — or settled empirical chains make long-horizon outcomes foreseeable — quality is derivation, not deliberation. Substituting workshop, vote, or seniority for derivation is vote on physics. Mechanism 5 in Strengthening the Commitment Boundary.

Corpus stance

A1 — adopted on this site: Reconciles tier-2 “logically necessary given evidence” with the atomicity ladder: necessity is about defeasibility of the claim relative to substrate, not about sitting at L0.