Powersets are too nice for pure set models; ordered set models are richer and can capture more computational behaviors.

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

• Down-sets are more convenient than up-sets for many purposes in order theory.claim0.758
  Observation that ↓ operator is easier to work with than ↑ due to order-preservation rather than order-reversal.
• How can order relations in posets provide semantic models for data and computation?question0.733
  Motivating question throughout: using order theory to capture information flow, approximation, and program behavior.
• Partially Ordered Set (Poset)concept0.727
  Fundamental structure: a set with a reflexive, antisymmetric, transitive relation.
• Partial orders naturally represent partial information states in computation.hypothesis0.719
  Foundational hypothesis of Domain Theory: partial order structure (D, ⊑) captures information ordering without quantification.
• The non-set-theoretic nature of powerdomains in domain theory creates unresolved obstructions when lifting standard game-theoretic solution concepts to model rule-changing games.claim0.713
  Assessment of Vassilakis's domain-theoretic economic models.
• Powerset with Inclusion Orderconcept0.713
  Family of all subsets of a set X, ordered by set inclusion; serves as a canonical example of a complete lattice.
• The code-agent ordering (TrackerAgent > SetRaceAgent > EconomyAgent) shows information exploitation matters more than greedy quartet-chasing, which in turn outperforms conservative budgetingclaim0.713
  interpretation of what drives success among deterministic strategies
• Base models assign higher likelihood to typical-set (representative) sequences than to degenerate sequences under VS promptshypothesis0.709
  Assumption D.6 formalized in the theoretical framework; empirically validated with coin-flip typicality rating experiments