Logic Truth Table Generator mechanism

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

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