Description
Classical finite quantification with an explicit empty-domain admission flag.
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.
Classical finite quantification with an explicit empty-domain admission flag.
When to use this tool
Use Quantified Statement Empty Domain Policy 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 predicateValues, quantifier, allowEmpty. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read value, empty. Inspect value, empty before interpreting the associated values.
Accept quantifier all or some and require a nonempty predicateValues list unless allowEmpty. Return every value for all, some value for some, and empty on an empty list.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| predicateValues | Predicate Values | Required. Array of boolean; maximum items 256. |
| quantifier | Quantifier | Required. Text; one of "all", "some"; maximum UTF-16 length 8192. |
| allowEmpty | Allow Empty | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| value | Value | Required. Boolean. |
| empty | Empty | Required. Boolean. |
{
"input": {
"predicateValues": [],
"quantifier": "all",
"allowEmpty": true
},
"output": {
"value": true,
"empty": true
}
}Limitations and assumptions
- When empty input is allowed, all is true and some false. The chosen empty-domain policy is explicit and no domain or predicate evaluation is performed.
- 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
- Philosophy: Quantified Statement Negation Rewrite
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.
- Quantifier Empty Domain Vacuity Token
Finite classical quantifier evaluation, including universal vacuity and false empty existential.