Check transitivity before inferring through chains…

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.

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.