Description
Apply the single outer classical quantifier negation rule to an explicitly supplied opaque predicate and bound-variable token; no parser, variable capture or theorem proving.
A logical calculation operates on a stated representation: truth values, token lists, counts, or an explicitly supplied relation. Checking one assignment, pair, trace, or witness is different from proving a formula or validating an entire argument. Empty domains, duplicate tokens, and scope conventions can change the result.
Apply the single outer classical quantifier negation rule to an explicitly supplied opaque predicate and bound-variable token; no parser, variable capture or theorem proving.
When to use this tool
Use Philosophy: Quantified Statement Negation Rewrite when you need this exact local truth, count, token, relation, or witness check within a larger logic workflow.
How to use the tool and how it works
- Enter quantifier, variable, predicate. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Accept quantifier forall or exists, an ASCII variable beginning with a letter followed by letters, digits, or underscores, and a nonblank predicate. Swap quantifier, preserve variable, and wrap the original predicate text as not (predicate) inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| quantifier | Quantifier | Required. Text; one of "forall", "exists". Implementation limit: 8192 Unicode code points and 16384 UTF-16 code units. |
| variable | Variable | Required. Text. Implementation limit: 8192 Unicode code points and 16384 UTF-16 code units. |
| predicate | Predicate | Required. Text. Implementation limit: 8192 Unicode code points and 16384 UTF-16 code units. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the calculated result members described below. | Required. Object. |
| result.negatedQuantifier | Negated Quantifier | Calculated result member: string. |
| result.variable | Variable | Calculated result member: string. |
| result.negatedPredicate | Negated Predicate | Calculated result member: string. |
{
"input": {
"quantifier": "forall",
"variable": "x",
"predicate": "P(x)"
},
"output": {
"result": {
"negatedQuantifier": "exists",
"variable": "x",
"negatedPredicate": "not (P(x))"
}
}
}Limitations and assumptions
- This is a textual quantifier-negation rewrite. It does not parse predicate syntax, simplify existing negation, resolve scope, or prove semantic equivalence for malformed formula text.
- Outputs are nested inside result. Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Alternative or Complementary methods
Use a parser, scope-aware representation, model checker, or proof procedure when the supplied token or witness representation is insufficient. A local passing check should not be promoted to global validity.
References
Similar or alternative tools
- Quantified Statement Empty Domain Policy
Classical finite quantification with an explicit empty-domain admission flag.
- Alpha Equivalence Bound Variable Pair
Compare flat single-binder token bodies, rejecting potential free-variable capture; nested binders are outside this model.