Check transitivity before inferring through chains — 'friend of friend' is not 'friend'
When a relationship type is mathematically transitive (like 'is greater than' or 'is ancestor of'), you can safely infer the endpoint connection from a chain; when it is not transitive (like 'is friend of' or 'is close to'), you must verify endpoint relationships directly rather than inferring them.
Why This Is a Rule
Transitive relationships allow chain inference: if A > B and B > C, then A > C (safe inference). Non-transitive relationships do not: if A is friends with B and B is friends with C, A is NOT necessarily friends with C (unsafe inference). The brain defaults to treating all relationships as transitive, producing reasoning errors when non-transitive relationships are chained.
This matters for practical reasoning because many important relationships are non-transitive: trust ("I trust A, A trusts B" does not imply "I trust B"), influence ("A influences B, B influences C" does not imply "A influences C in the same way"), agreement ("A agrees with B on X, B agrees with C on X" does not imply "A agrees with C on X"), and proximity ("A is close to B, B is close to C" does not imply "A is close to C").
Chaining non-transitive relationships produces confident but wrong inferences. The chain feels logical — each link is valid — but the endpoint inference is not guaranteed. The fix: check whether the relationship type is transitive before inferring through chains.
When This Fires
- When reasoning through chains of relationships ("since A relates to B and B relates to C...")
- During organizational reasoning (reporting chains, influence networks, trust chains)
- When making introductions or referrals based on indirect connections
- Any chain reasoning where the endpoint inference might not hold
Common Failure Mode
Assuming all chains are transitive by default: "My manager's priorities should be my director's priorities, which should be the VP's priorities." The "reports to" relationship is transitive, but "shares priorities with" is not — priorities shift at each management level. Chaining "reports to" and inferring "shares priorities" produces misaligned work.
The Protocol
When inferring through a chain: (1) Identify the relationship type being chained. (2) Test transitivity: if A→B and B→C, does A→C necessarily follow? (3) Transitive (is-greater-than, is-ancestor-of, is-prerequisite-for) → safe to infer endpoints. (4) Non-transitive (is-friend-of, trusts, agrees-with, is-close-to) → must verify endpoint relationship directly. The chain doesn't guarantee it. (5) When in doubt, verify. The cost of checking is minutes; the cost of a wrong inference can be a misaligned project or a broken trust assumption.