Read mechanism against mechanism, ACH and expert-system backward chaining are a false friend: a flat matrix scan versus a goal-directed recursive proof search

embedding-false-friendcross-domain-bridgeACHbackward-chainingexpert-systemsreasoning-by-eliminationmechanism-comparisonbridge-investigation

The vault has long held that ACH's Step 5 rhymes with backward chaining — both get called "elimination," both were developed in the 1970s — and that no source has ever drawn the comparison. That earlier note is a documented-absence finding: nobody wrote it down. This note does the thing the absence left undone — it compares the two mechanisms directly, from their Tier-1 primaries — and finds the resemblance is a mechanism-level false friend.

Backward chaining, per MYCIN's own technical account, is a sequential, goal-directed, recursive proof search: pick one target, retrieve the rules whose conclusions bear on it, and chain through premise subgoals until each resolves (claim-mycin-backward-chaining-is-goal-directed-recursive-subgoal-search). ACH is a flat, exhaustive consistency scan: enumerate every hypothesis up front, score each evidence item against all of them in a matrix, and eliminate by tallying inconsistency — no rule base, no conclusion-indexed retrieval, no recursive subgoaling (claim-ach-matrix-scores-each-evidence-item-against-every-hypothesis). Sharing the word "eliminate" is not sharing the mechanism: one focuses on a single proof tree, the other refuses to focus at all. This joins the vault's tracked false-friend series (observation-ach-abduction-lucky-widrow-cosine-pairing-is-embedding-false-friend), but is reached by reading the algorithms rather than by failing to find a citation.

The verification that would move this past an echo — a primary or scholarly source that actually draws the ACH↔backward-chaining comparison — is tracked at question-ach-backward-chaining-structural-echo. The through-line note observation-reasoning-by-elimination-from-stoic-logic-to-symbolic-ai still lines ACH and backward chaining up as one lineage of "eliminate the impossible"; the mechanism read here suggests that lineage is coarser than the algorithms underneath it, and the parent note's own Step-5↔chaining span remains the unsourced one.