Source: https://guthlabs.ai/docs/instruments/logic-truth-table-generator/mechanism/

instrument mechanism / verified-clean

# Logic Truth Table Generator mechanism

The inspectable method record for Logic Truth Table Generator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The core algorithm is mathematically correct, but the instrument is not fully specified enough for deterministic parsing and evaluation. Add a formal grammar, precedence table, associativity rules, token conventions, validation behavior, row-order convention, and explicit semantics for constants and zero-variable expressions before release.

- Exhaustive evaluation over 2^n assignments is the standard method for truth tables, tautology checks, contradiction checks, and satisfiability checks.

- The specification does not define operator precedence or associativity, so expressions such as p OR q AND r may have multiple parses.

- The specification does not define the exact token syntax, case sensitivity, implication direction, XOR arity, IFF associativity, or whether parentheses are required.

- The specification does not define behavior for malformed expressions, duplicate variables, variables appearing in the expression but absent from the variable list, constants, or an empty variable list.

## Units and conventions

- Boolean values are unitless and represented as false/0 and true/1.

- The test vectors assume variables are listed in the stated order and rows are generated in binary order from all-false to all-true, with the first listed variable as the most-significant bit.

- The test vectors assume NOT has highest precedence, AND precedes OR/XOR, and parentheses explicitly determine the intended grouping.

- IMPLIES is interpreted as A IMPLIES B = (NOT A) OR B; IFF is true exactly when both operands have equal truth values; XOR is true exactly when exactly one operand is true.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "expression": "p AND (q OR NOT r)",
    "variables": [
      "p",
      "q",
      "r"
    ]
  },
  "expected_outputs": {
    "truth_table": [
      {
        "p": false,
        "q": false,
        "r": false,
        "result": false
      },
      {
        "p": false,
        "q": false,
        "r": true,
        "result": false
      },
      {
        "p": false,
        "q": true,
        "r": false,
        "result": false
      },
      {
        "p": false,
        "q": true,
        "r": true,
        "result": false
      },
      {
        "p": true,
        "q": false,
        "r": false,
        "result": true
      },
      {
        "p": true,
        "q": false,
        "r": true,
        "result": false
      },
      {
        "p": true,
        "q": true,
        "r": false,
        "result": true
      },
      {
        "p": true,
        "q": true,
        "r": true,
        "result": true
      }
    ],
    "tautology": false,
    "satisfiable": true,
    "contradiction": false
  },
  "working": "Evaluate rows in binary order. For 000: NOT r = 1; q OR NOT r = 0 OR 1 = 1; p AND 1 = 0 AND 1 = 0. For 001: NOT r = 0; 0 OR 0 = 0; 0 AND 0 = 0. For 010: NOT r = 1; 1 OR 1 = 1; 0 AND 1 = 0. For 011: NOT r = 0; 1 OR 0 = 1; 0 AND 1 = 0. For 100: NOT r = 1; 0 OR 1 = 1; 1 AND 1 = 1. For 101: NOT r = 0; 0 OR 0 = 0; 1 AND 0 = 0. For 110: NOT r = 1; 1 OR 1 = 1; 1 AND 1 = 1. For 111: NOT r = 0; 1 OR 0 = 1; 1 AND 1 = 1. The results contain at least one true row, so satisfiable = true. They are not all true, so tautology = false. They are not all false, so contradiction = false."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The 31-variable extreme case requires 2,147,483,648 truth-table rows. If the instrument attempts to allocate or generate that table without rejecting the input, it can exhaust memory, hang, or overflow its row-count representation. The precedence probe also exposes a correctness hazard if NOT/AND precedence is undocumented or parsed inconsistently.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/logic-truth-table-generator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/logic-truth-table-generator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/logic-truth-table-generator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`