all-semantic-edge-cases-are-uniform
IN derived (depth 3)
All semantic edge cases — absence of justifications yielding premise behavior, absence of nodes producing asymmetric fail semantics, and empty antecedent lists satisfying vacuous truth — emerge from the same uniform evaluation rules without special-case handling, including the emergent disjunctive-over-conjunctive truth structure.
Summary
When something is missing or absent in the system — whether a node has no justifications, references a node that does not exist, or has an empty list of requirements — the system handles all of these edge cases through the same uniform evaluation rules rather than through special-case code paths. This matters because it means the system's behavior at its boundaries is predictable and consistent, arising naturally from its core logic rather than from a patchwork of exception handling.
Justifications
SL — depth-3 — both normal truth semantics and edge-case absence semantics derive from the single evaluation rule without branching
Antecedents (all must be IN):
- truth-semantics-are-emergent-and-uniform — Truth maintenance semantics are fully emergent from simple uniform rules: premise behavior arises from empty justification lists, evaluation is pure and type-agnostic across SL/CP, and node truth is a clean disjunction-of-conjunctions — no special cases exist anywhere in the evaluation path.
- absence-has-consistent-dual-semantics — Absence has deliberate, defined semantics throughout the system at two levels: structural absence (no justifications) creates premise behavior via vacuous truth over empty lists, while referential absence (missing nodes) follows conservative/permissive asymmetry — both forms of absence produce predictable behavior rather than errors or undefined state.
Dependents
These beliefs depend on this one:
- belief-revision-covers-all-cases-uniformly — The belief revision system handles normal beliefs and all edge cases (premises from absent justifications, asymmetric missing-node semantics, vacuously valid empty antecedents) through the same minimal mechanisms (outlist defeat and dependency-directed backtracking) — no edge case requires special-case logic.