An AI logic audit checks what changes when a proposed rule moves the parentheses. Use six fictional Boolean records to save intermediate calculations, exact selected sets and a counterexample showing that two specified expressions are not equivalent.
Which two parenthesized rules are being compared?
An AI logic audit should preserve the grouping of the source rule before judging a proposed rewrite. AND requires all its joined conditions to be true. OR here is inclusive: at least one true condition is enough, and two true conditions also produce true. The words are short, but grouping them differently can change the result.
The source is P AND (Q OR R). The prewritten proposal is (P AND Q) OR R. Both expressions contain explicit parentheses. We are not inferring an intended rule from ambiguous prose or assuming a platform’s default operator precedence. Parentheses identify the inner operation to calculate before combining its result with the remaining input.
P, Q and R are stipulated true-or-false flags on fictional practice tokens. They do not represent a person’s eligibility, consent, security clearance or an actual audience filter. No model generated these inputs. This is a manual exercise, not an observed Excel calculation, application test or live selection action.
Write the boundary first: “Practice V1; B1–B6 only; known Boolean inputs; preserve both expressions; show intermediate and final values for every ID.” Boolean means a value with the two states true and false. The artificial intelligence guide covers the broader topic. This audit instead produces a saved evaluation trace and a concrete counterexample to one specific equivalence claim.
Preserve the six-case source card without extending it
The English exercise uses six supplied records in the order below. T means true and F means false. Keep the source identifiers attached to their three input values when copying them. A table that looks tidy but attaches one record’s result to another identifier does not preserve the evidence.
Six cases are not an exhaustive truth table for three Boolean inputs: there are eight possible combinations. We deliberately do not supply every combination here. Do not turn a six-case inspection into a claim that all possible inputs have been tested. A counterexample can still disprove equivalence without exhaustive testing.
| ID | P | Q | R |
|---|---|---|---|
| B1 | F | T | T |
| B2 | T | F | T |
| B3 | F | F | F |
| B4 | T | T | F |
| B5 | F | F | T |
| B6 | T | F | F |
B1 has P false while Q and R are true. B5 has P false, Q false and R true. Retain those cases even if they initially seem uninteresting. They will expose the difference between requiring P in the source and allowing the final OR branch in the proposal to determine the result.
Unknown flags, missing cells, text pretending to be a logical value and errors are outside the card. If one appears in a real source, leave its interpretation unresolved rather than silently coercing it to false. The Excel prompt templates address broader written calculation requests. No spreadsheet formula is executed in this account-free text-and-calculator exercise.
How do you calculate the two intermediate branches?
For the source, first evaluate Q OR R. If either input is true, including when both are true, that intermediate result is true. It is false only when Q and R are both false. Then join that result with P using AND. The source cannot produce true when P is false, because AND requires both operands to be true.
For the proposal, evaluate P AND Q first. Its intermediate value is true only when both inputs are true. Then combine that result with R using OR. In this grouping, a true R can make the final result true even when P is false. The change is structural, not a new fact about any input.
| ID | Q OR R | P AND (Q OR R) | P AND Q | (P AND Q) OR R |
|---|---|---|---|---|
| B1 | T | F | F | T |
| B2 | T | T | F | T |
| B3 | F | F | F | F |
| B4 | T | T | T | T |
| B5 | T | F | F | T |
| B6 | F | F | F | F |
Read B1 step by step. Q OR R is true, but P AND true is false because P is false. In the proposal, P AND Q is false, then false OR R is true. The same three supplied flags therefore yield different final values. Neither input correction nor a model run is required to establish that disagreement.
Now read B2 and B4 rather than stopping after the first mismatch. They show how the expressions can agree for some records despite not being equivalent in general. A successful case does not cancel a counterexample. The dependency audit checks all required predecessors and graph waiting states; this task has no predecessor graph, schedule, duration or evolving task state.
Which exact ID sets and counterexample must be retained?
The source produces true for B2 and B4: two supplied records. The proposal produces true for B1, B2, B4 and B5: four records. Write the complete selected sets before their counts. The mismatch list is B1 and B5. For this particular supplied card, the proposal adds two true results and does not lose either source-selected record.
Counts alone are not enough. Two different rules could select equal numbers of records but select different identifiers. Keep a per-ID comparison so that agreement is about the same records, not merely an equal total. The selected-set comparison is a check on the evaluation trace, not a substitute for showing the inner operations.
A counterexample is a concrete input that contradicts a general equivalence claim. Use B5: P is false, Q is false and R is true. The source yields false; the proposal yields true. One such input establishes that these two specified expressions are not equivalent over all Boolean inputs. It does not establish that all regrouping is wrong or that every live implementation is faulty.
The classification error ledger compares prewritten reference and proposed labels, then counts four outcome types and three rates. This audit derives two outputs from three input flags through explicitly grouped intermediate operations. Do not add a confusion matrix, a model accuracy percentage or a performance claim to make the task seem broader.
How should the three proposed claims be judged?
Claim one says: “A true R always makes the source result true.” Reject it. B1 and B5 both have true R and false P, so the source remains false. Cite the relevant source trace. Explaining where R sits inside the parentheses is more useful than replacing the answer without identifying the reason.
Claim two says: “Moving the parentheses preserves the rule.” Reject that statement for these two expressions. B5 is a witness with differing results under unchanged inputs. Keep the conclusion specific: the source and proposal here are not equivalent. Other expressions may admit valid equivalent rewrites, so do not turn this example into a universal ban on regrouping.
Claim three says: “This saved calculation proves our platform’s real filter works correctly.” Mark it unsupported. No platform configuration, actual input typing, runtime behavior or additional rules have been inspected. Correct manual arithmetic does not become an observation of a deployed system simply because an assistant describes it confidently.
Microsoft’s AND and OR pages support the meanings of the operations. They are two pages from one authority, not independent institutions. Our written exercise supplies the grouping; the pages are not evidence of every platform’s default precedence or null-handling behavior. The Typeform routing guide concerns question paths, first matching rules and endings. This fixed-expression calculation does not construct or validate those routes.
What evidence should survive saving and reopening?
On Windows, open Start, type Notepad and launch the editor. Head the file “Grouped AND OR audit V1.” Copy both expressions with their parentheses, followed by the six source records and the four intermediate/final columns. Add the exact source-selected set, proposal-selected set and mismatch IDs.
Before saving, include all three claim decisions and their supporting evidence. Write the B5 counterexample explicitly as P false, Q false, R true; source false, proposal true. Add the limitation that six cases are not exhaustive and no real system was run. Press Ctrl+S, choose Documents and save as grouped-logic-audit-V1.txt.
Close the editor and reopen the saved file from that folder. Confirm that parentheses have not moved, B5 remains a mismatch, the selected sets retain their identifiers, and the six-case limitation is visible. A file containing only “two versus four” is not the completed artifact because it cannot reconstruct why the rules differ.
For an optional second opinion, supply only the fictional card to an assistant you already use. Ask: “Preserve both parenthesized expressions. Show Q OR R, source result, P AND Q and proposal result for every ID. List exact selected sets and mismatch IDs. Give a concrete counterexample to equivalence. Do not invent missing cases or claim a live filter or model test.” If that comparison was not performed, record it as not performed.
A suggested fifteen-minute allowance gives three minutes to boundaries, five to the trace, three to claims and four to saving and reopening. It is a cognitive plan, not a measured participant result or guaranteed completion time. In earlier public writing about perfection and effectiveness, I described delays caused by pursuing every detail. Here that principle means finishing one explainable evidence file, not claiming personal application testing or customer outcomes.
Frequently asked questions
Is OR exclusive in this exercise?
No. It is inclusive: either true input suffices and two true inputs also produce true.
Why does B5 disprove equivalence?
Its unchanged inputs produce false under the source grouping and true under the proposal grouping. Equivalent expressions cannot disagree on the same input.
Do equal selected counts prove equal rules?
No. Equal counts can hide different selected identifiers. Compare exact sets and retain each record’s intermediate calculation.
Does the six-case card cover all possible inputs?
No. Three Boolean inputs have eight possible combinations. The six supplied cases are enough to contain a counterexample, not to claim exhaustive testing.
