Description
Compare supplied premise arity under an explicit duplicate policy; no inference validity judgment.
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.
Compare supplied premise arity under an explicit duplicate policy; no inference validity judgment.
When to use this tool
Use Inference Premise Arity Gap 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 premiseIds, requiredArity, duplicatesCountSeparately. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read effectiveArity, gap, matches. Inspect matches before interpreting the associated values.
For nonnegative integer requiredArity count premiseIds separately if duplicatesCountSeparately, otherwise count distinct IDs. Return effectiveArity, gap=effectiveArity-requiredArity, and matches on equality.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| premiseIds | Premise Ids | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| requiredArity | Required Arity | Required. Safe integer; minimum 0. |
| duplicatesCountSeparately | Duplicates Count Separately | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| effectiveArity | Effective Arity | Required. Safe integer. |
| gap | Signed difference under the stated formula and measurement unit. | Required. Safe integer. |
| matches | Matches | Required. Boolean. |
{
"input": {
"premiseIds": [
"p",
"p",
"q"
],
"requiredArity": 2,
"duplicatesCountSeparately": false
},
"output": {
"effectiveArity": 2,
"gap": 0,
"matches": true
}
}Limitations and assumptions
- This compares premise counts under the supplied duplicate policy. It does not check premise truth, rule applicability, types, or inference validity.
- 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. Signed zero is exported as zero.
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
- Alpha Equivalence Bound Variable Pair
Compare flat single-binder token bodies, rejecting potential free-variable capture; nested binders are outside this model.
- Argument Assumption Scope Depth
Audit explicit opening/closing assumption-scope actions without evaluating argument validity.