Tetravalent Logic

Tetravalent Logic

Demerzel uses four-valued logic for uncertainty-aware reasoning. Unlike binary true/false, tetravalent logic explicitly represents incomplete knowledge and conflicting evidence.

Values

Value	Symbol	Meaning	Action
True	T	Verified with evidence	Proceed with confidence
False	F	Refuted with evidence	Act on the negation
Unknown	U	Insufficient evidence	Investigate before acting
Contradictory	C	Conflicting evidence	Escalate — cannot resolve automatically

Why Four Values?

Binary logic forces premature commitment. When Demerzel doesn't know whether a consumer repo is compliant, the answer isn't "true" or "false" — it's unknown, which triggers investigation rather than false confidence or false alarm.

Contradictory is the most important value. When evidence conflicts (e.g., a test passes but logs show violations), the system cannot resolve it — a human must decide which evidence to trust.

Belief State Schema

{
  "proposition": "ix governance integration is current",
  "value": "U",
  "confidence": 0.40,
  "evidence": ["submodule 142 commits behind", "ix-governance crate exists"],
  "updated_at": "2026-03-17",
  "previous_value": null
}

Truth Tables

AND (conjunction)

AND	T	F	U	C
T	T	F	U	C
F	F	F	F	F
U	U	F	U	C
C	C	F	C	C

OR (disjunction)

OR	T	F	U	C
T	T	T	T	T
F	T	F	U	C
U	T	U	U	C
C	T	C	C	C

NOT (negation)

Value	NOT
T	F
F	T
U	U
C	C

Integration with Confidence

Tetravalent values combine with confidence scores:

• T at 0.95 = strong verified belief → act autonomously
• T at 0.60 = weakly verified → proceed with note
• U at 0.50 = uncertain → investigate
• F at 0.90 = strongly refuted → act on negation
• C at any = conflicting → escalate to human

Conscience Integration

The conscience system monitors tetravalent state transitions:

• T → F = Something believed true was proven false → confidence_discomfort signal
• T → U = Certainty degraded → stale_action_discomfort if actions were taken
• Any → C = Contradiction emerged → immediate escalation