Vacuous Truth Empty Domain Universal Checker
Classical universal truth from complete finite domain/counterexample counts; empty domain allowed explicitly, no natural-language truth inference.
Description
Vacuous Truth Empty Domain Universal Checker: return universal satisfied, vacuously satisfied.
A universal statement says that every member of a domain satisfies a predicate. On an empty domain it has no counterexamples and is vacuously satisfied.
This tool returns universal satisfied, vacuously satisfied. Use the stated units and model convention when interpreting these fields.
When to use this tool
Use this tool when the supplied inputs match the specific operation described above and you need a repeatable result under its stated convention.
- Check the supported input and output contract against an existing calculation or observation.
- Use the complete example to confirm units, selector spelling and result interpretation.
How to use the tool and how it works
- Enter every field in the input table using the stated units and the exact supported selector spelling where applicable.
- Run the tool. Correct input errors before interpreting an output.
- Read the result fields below; use accompanying flags and the stated sign, boundary or model convention when interpreting a number.
Check that domainSize and falsePredicateInstances are bounded nonnegative integers with counterexamples no greater than domain size. Return universalSatisfied when counterexamples equal zero and vacuouslySatisfied when domain size equals zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| domainSize | Domain size. | Integer; from 0 to 1000000000 inclusive |
| falsePredicateInstances | False predicate instances. | Integer; from 0 to domainSize inclusive |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.universalSatisfied | Universal satisfied flag under the exact conditions described above. |
| result.vacuouslySatisfied | Vacuously satisfied flag under the exact conditions described above. |
{
"input": {
"domainSize": 0,
"falsePredicateInstances": 0
},
"output": {
"result": {
"universalSatisfied": true,
"vacuouslySatisfied": true
}
}
}Limitations and assumptions
- The tool relies on caller-supplied counts and does not enumerate the domain or evaluate a predicate.
- Every declared field is required and unexpected fields are rejected. Numeric inputs must be finite; input errors are distinct from a valid false result or an explicitly qualified output.
- Extremely large inputs and nonfinite or excessively large outputs are rejected. List positions reported by the tool use zero-based indices unless stated otherwise.
Alternative or Complementary methods
Check the underlying observations, units and conventions independently before using the result in a larger workflow. The tools listed below address nearby tasks; compare their inputs and scope before substituting one for this operation.
References
Similar or alternative tools
- cnf clause set from truth table builder
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- truth table row count 2n
A truth table has one row for every assignment of its Boolean variables.