S001 · implies
Before
source roles = [qf-proof-modus-tollens, [conclusion, inference_rule, p, premises, q]]
After
derived = [BASE-no-required-operation, no-invented-domain]
Conditions: none
Check THIS bank’s keys/operation/domain:legacy table underscores,MOD50 local hyphens;permissive BASE data acquires no unknown-field restriction.Keep Number.isInteger and SAFE source guards distinct,while preserving ORIGINAL JSON number representations.
Step identifiers and dependencies
Rule: R67_SOURCE_specific_keys_operation_domain_and_numeric_bank · Uses: G001
S002 · implies
Before
source roles = [modus_tollens, [P→Q, ¬Q], ¬P]
After
derived = [[P, Q, P->Q, second premise, both premises, conclusion], [[No, No, Yes, Yes, Yes, Yes], [No, Yes, Yes, No, No, Yes], [Yes, No, No, Yes, No, No], [Yes, Yes, Yes, No, No, No]], Yes]
Conditions: none
Treat P/Q as GENERAL proposition symbols,without adding extra arithmetic relations between their illustrative texts.Use the displayed COLUMN LABELS to audit ALL four valuations.Validity requires a true conclusion in EVERY row satisfying BOTH premises.This neither proves the premises factually true nor establishes causation.
Step identifiers and dependencies
Rule: Proof_FULL_truth_table_premise_satisfaction_THEN_conclusion · Uses: G001, S001
S003 · implies
Before
source roles = [modus_tollens, [P→Q, ¬Q], ¬P]
After
derived = [Yes]
Conditions: none
MP:given P and P→Q,infer Q.MT:assuming P would give Q,contradicting¬Q,so infer¬P.Both preserve the DECLARED premises and do not use an unproved converse.
Step identifiers and dependencies
Rule: Proof_VALID_MP_or_MT_natural_inference_under_declared_premises · Uses: G001, S002