absence-has-consistent-dual-semantics
IN derived (depth 2)
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.
Summary
The system handles "things that aren't there" in two deliberate ways rather than treating them as errors. When a node has no justifications at all, it quietly acts like a premise — something assumed true by default. When the system references a node that doesn't exist, it plays it safe for inputs (rejecting unknown dependencies) but stays lenient for outputs (not failing just because a downstream consumer is missing). Together, these rules mean absence is never ambiguous or crashy — it always resolves to a predictable outcome.
Justifications
SL — Structural absence (depth-1) and referential absence (depth-1) are independently well-defined, and together show the system treats all forms of absence as meaningful semantic choices
Antecedents (all must be IN):
- premise-behavior-emerges-from-absence — Premise behavior is not explicitly implemented — it emerges from three defaults: nodes with no justifications default to IN, empty antecedent lists are vacuously valid, and the system preserves a premise's current truth value rather than deriving it.
- missing-nodes-have-asymmetric-fail-semantics — Missing nodes are treated asymmetrically: absent antecedents fail validation (conservative), absent outlist nodes pass (permissive), creating a "believe unless proven otherwise" default
Dependents
These beliefs depend on this one:
- absence-and-outlist-form-complete-negative-semantics — The system has complete semantics for all forms of negation: structural absence produces emergent premise behavior and asymmetric fail modes, while explicit outlist entries provide conjunctive defeat with defined absent-node handling and persistence — together covering every mechanism by which beliefs can be negated or defeated.
- all-semantic-edge-cases-are-uniform — 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.