Description
Finite classical quantifier evaluation, including universal vacuity and false empty existential.
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.
Finite classical quantifier evaluation, including universal vacuity and false empty existential.
When to use this tool
Use Quantifier Empty Domain Vacuity Token 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 truths, quantifier. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read truth, emptyDomain. Inspect truth, emptyDomain before interpreting the associated values.
For quantifier all return truths.every(Boolean); for exists return truths.some(Boolean). Return emptyDomain when truths is empty.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| truths | Truths | Required. Array of boolean; maximum items 256. |
| quantifier | Quantifier | Required. Text; one of "all", "exists"; maximum UTF-16 length 8192. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| truth | Truth | Required. Boolean. |
| emptyDomain | Empty Domain | Required. Boolean. |
{
"input": {
"truths": [],
"quantifier": "all"
},
"output": {
"truth": true,
"emptyDomain": true
}
}Limitations and assumptions
- On an empty domain all is true and exists is false. Predicate truth values and domain membership are supplied rather than parsed or inferred.
- 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.
- Modal Box Vacuous Successor Case
Evaluate box and diamond on an explicit finite list of accessible successor truth values.