truth-is-disjunctive-over-conjunctive-rules
IN derived (depth 1)
A node's truth is a disjunction over justifications (any valid justification makes it IN), where each justification is a conjunction (all antecedents IN and all outlist OUT), and any-mode explicitly reifies OR semantics as per-premise justifications.
Summary
A node is considered true if at least one of its supporting reasons holds up, and each individual reason holds up only when all of its positive dependencies are true and all of its negative dependencies are false. The "any mode" feature makes this OR logic explicit by giving each supporting premise its own independent reason, so a single valid premise is enough to keep the node true.
Justifications
SL — These three beliefs collectively define the DNF (disjunctive normal form) evaluation model at the heart of truth computation
Antecedents (all must be IN):
- node-in-if-any-justification-valid — A Node is IN when at least one of its Justifications is valid; a Justification is valid when all antecedents are IN and all outlist nodes are OUT (disjunctive over justifications, conjunctive within each).
- sl-justification-semantics — An SL justification is valid iff ALL antecedents are IN AND ALL outlist nodes are OUT; a node is IN iff ANY of its justifications is valid (conjunction within a justification, disjunction across justifications).
- any-mode-creates-per-premise-justifications — When `any_mode=True` and multiple antecedents are given, each antecedent gets its own SL justification (OR semantics: node is IN if *any* antecedent is IN), rather than the default single multi-antecedent justification (AND semantics).
Dependents
These beliefs depend on this one:
- 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.