Rules and revision operations
Rules activate from base facts. Beliefs retain support history. v1 uses no RHP (Retraction + History-based Propagation): restored values do not activate new rules during retraction. Final CF rule propagation is a separate operation.
T = True · F = False · U = Unknown · Purple border = CF target · Shaded node = focus of the selected stage.
The full support graph stays visible. Crossed-out values show the previous state; colored regions separate upstream support, old consequences and new computation.
A Activation & propagation · R Retraction · C Counterfactual assignment & computation
A-1 Activation order
Rules activate from base facts, following graph dependencies. Applicable rules with lower rule numbers activate first.
Illustrative example · select a stage to inspect its state. A-2 Most recent support wins
The most recently activated valid support determines a node’s truth value. Values assigned by earlier rules remain recorded in its history with their justifications.
Illustrative example · select a stage to inspect its state. A-3 Retraction + History-based Propagation · RHP
RHP (Retraction + History-based Propagation) resolves surviving history with an aggregation rule after retraction, then activates rules from the restored value. The aggregation rule can vary; this example uses Recency. v1 retains history restoration but disables RHP.
Illustrative example · select a stage to inspect its state. History aggregation rules
The value restored from history can be determined by different aggregation rules:
Aggregation How a value is selected Recency Select the newest surviving valid support. Majority Select the polarity supported by more surviving valid records. Alternative Select surviving support for the opposite polarity of the retracted belief, regardless of history order. Weight Recency Combine support weights and recency when resolving the surviving history. These are possible aggregation rules for RHP. v1 uses Recency for restoration and does not perform RHP.
R-1 Retraction removes support
Retracting the current belief removes its governing support. The next most recent valid support becomes active; it may assign the same truth value again. The node becomes U only when no valid support remains. Retracted records remain visible in the audit history but no longer support the belief.
Illustrative example · select a stage to inspect its state. R-2 Forward retraction
After the CF target changes value, retract downstream support that depended on its old value. At each node, restore the newest remaining valid support; if none remains, the value becomes U. Continue downstream as support becomes invalid. Do not activate new rules during this step.
Illustrative example · select a stage to inspect its state. Forward retraction without RHP
The propagation described in Rule A-3 is not performed during forward retraction: a changed or restored value does not activate new rules or create new downstream beliefs. Existing support is still checked, invalid support is retracted, and surviving support may restore a value. v1 uses this no-RHP policy; recency restoration remains enabled.
R-3 Backward retraction · Cut depth
Backward retraction removes selected upstream support along the CF target’s initial governing support path. Cut depth specifies how far upstream to retract: each additional 0.5 alternates between cutting an edge and retracting a signed belief. Affected nodes resolve from their remaining valid support.
Illustrative example · select a stage to inspect its state. - 0.5 · Edge
- Disable the incoming rule to the CF target.
- 1.0 · Signed belief
- Also retract the nearest upstream node’s initial signed belief.
- 1.5 · Next edge
- Also disable the next upstream rule.
- 2.0 · Next signed belief
- Also retract the next upstream node’s initial signed belief.
An edge-only cut leaves its source belief intact. A signed-belief cut disables all incoming rules and base facts supporting the selected polarity; opposite support is preserved. Resolve affected nodes from surviving history and maintain dependent support.
RHP after backward retraction
These are two alternative policies after a backward cut:
With RHP. Perform the propagation in Rule A-3: a changed or restored value can activate new rules and compute new downstream beliefs.
Without RHP. Skip that fresh propagation. Retract invalid support and restore surviving support, but do not activate new rules from the restored value. This is the v1 dataset policy.
C-1 CF target assignment
Add the requested counterfactual value directly to the selected target, without a rule justification. Existing rule support and its history remain recorded. The external CF assignment determines the target’s current value.
Illustrative example · select a stage to inspect its state. C-2 Assign CF and recompute
Use the protected external CF assignment for final computation. Continue downstream only when a node’s truth value changes; restored values from retraction are not separate computation seeds.
Illustrative example · select a stage to inspect its state.