system-semantics-are-minimal-and-complete
IN derived (depth 3)
The entire TMS — both monotonic truth maintenance and non-monotonic defeat — derives from a minimal set of uniform primitives: emergent truth rules (disjunction over conjunction, premise-from-absence) combined with a single reversible outlist mechanism that underlies all defeat features, with no additional machinery required.
Summary
The whole system runs on surprisingly few moving parts. Truth values emerge from simple uniform rules, and every form of defeat or retraction traces back to one reversible mechanism. Nothing extra was bolted on — the minimal primitives compose to produce all the complex behaviors, which means the system has no hidden complexity or special-case machinery that could harbor subtle bugs.
Justifications
SL — Monotonic semantics (depth-2) + non-monotonic semantics (depth-2) together prove the full system is both minimal and complete — every behavior emerges from a small shared rule set
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.
- non-monotonic-system-is-single-reversible-primitive — The entire non-monotonic reasoning system — challenges, kill-switches, supersession, and dialectics — is built on a single primitive (outlist) that is inherently reversible, with no dedicated machinery for any defeat pattern.
Dependents
These beliefs depend on this one:
- semantic-minimality-with-operational-determinism — The system unifies semantic minimality (all non-monotonic features and truth semantics derive from uniform outlist/disjunction primitives) with operational determinism (all operations terminate predictably via BFS fixpoint with conservative failure semantics), yielding a small trusted kernel that powers all reasoning.
- semantics-and-revision-share-minimal-foundations — Both truth maintenance semantics and belief revision achieve comprehensive coverage through the same minimal primitives — the outlist primitive simultaneously enables emergent truth evaluation (disjunction over conjunction with absence semantics) and all non-monotonic revision mechanisms (defeat, backtracking, dialectics), confirming minimality as a cross-cutting architectural principle rather than a property of any single subsystem.
- system-is-minimal-sound-and-scalable — The entire system — from single-node truth semantics through multi-agent operation — achieves semantic minimality (all features derive from uniform primitives), operational soundness (deterministic reversible truth maintenance), and safe scalability (isolated multi-agent operation) simultaneously.