Description
Expose empty-domain vacuity flags from a supplied domain size.
Formal annotations separate declared truth values, domain assumptions, variable lists and source interpretations. A direct self-reference differs from an indirect cycle, and one self-loop differs from a globally reflexive relation. Local token operations do not parse a complete argument, derive its assumptions or establish truth or validity.
Expose empty-domain vacuity flags from a supplied domain size.
When to use this tool
Use Quantifier Domain Emptiness Flag when you already have suppliedDomainSize and need to expose empty-domain vacuity flags from a supplied domain size.
How to use the tool and how it works
- Enter suppliedDomainSize. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read empty, universalVacuityApplies, existentialWitnessPossible. Inspect empty, universalVacuityApplies, existentialWitnessPossible before interpreting the associated values.
Require nonnegative safe whole size; empty and universalVacuityApplies mean size=0, existentialWitnessPossible means size>0.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| suppliedDomainSize | Supplied Domain Size | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| empty | Empty | Required. Boolean. |
| universalVacuityApplies | Universal Vacuity Applies | Required. Boolean. |
| existentialWitnessPossible | Nonempty supplied domain only; does not assert that a predicate has a witness. | Required. Boolean. |
{
"input": {
"suppliedDomainSize": 0
},
"output": {
"empty": true,
"universalVacuityApplies": true,
"existentialWitnessPossible": false
}
}Limitations and assumptions
- A nonempty domain permits a witness but does not prove a predicate has one; no domain or proposition is inspected.
- 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.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Parse or formalize the complete expression and declared semantics when validity is the question. Inspect the full reference or accessibility relation for cycles and global properties; a supplied annotation, self-loop or variable list establishes only its local predicate.
References
Similar or alternative tools
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