The order relation ≤ on a poset P is determined entirely by the down-sets in P.

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

• How can order relations in posets provide semantic models for data and computation?question0.804
  Motivating question throughout: using order theory to capture information flow, approximation, and program behavior.
• Partially Ordered Set (Poset)concept0.775
  Fundamental structure: a set with a reflexive, antisymmetric, transitive relation.
• Down-sets are more convenient than up-sets for many purposes in order theory.claim0.767
  Observation that ↓ operator is easier to work with than ↑ due to order-preservation rather than order-reversal.
• Partial orders naturally represent partial information states in computation.hypothesis0.756
  Foundational hypothesis of Domain Theory: partial order structure (D, ⊑) captures information ordering without quantification.
• Within a building, the rectilinear order also comes from a disciplined unfolding of the whole.claim0.743
• Order (general mathematical structure of space)concept0.741
  A most general system of mathematical structures arising from the nature of space, which has degrees of life.
• Within-agent score standard deviation suggests deck order matters more than seat position.claim0.731
  Observation from variance analysis, though not tested as hypothesis.
• Down-set (Order Ideal)concept0.731
  Subset Y of poset P closed downward under the order; dually related to up-sets.