Description
Apply an explicit numerical boundary; this does not resolve vague predicates.
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.
Apply an explicit numerical boundary; this does not resolve vague predicates.
When to use this tool
Use Sorites Explicit Threshold One Step 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 quantity, step, threshold, inclusive. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read before, after, crosses. Inspect before, after, crosses before interpreting the associated values.
Compare quantity and quantity+step against threshold using >= if inclusive, otherwise >. Return before, after, and crosses when the two Boolean comparisons differ.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| quantity | Quantity | Required. Finite number. |
| step | Step | Required. Finite number. |
| threshold | Threshold | Required. Finite number. |
| inclusive | Inclusive | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| before | Before | Required. Boolean. |
| after | After | Required. Boolean. |
| crosses | Crosses | Required. Boolean. |
{
"input": {
"quantity": 9,
"step": 1,
"threshold": 10,
"inclusive": true
},
"output": {
"before": false,
"after": true,
"crosses": true
}
}Limitations and assumptions
- A negative step can cross in the reverse direction. The explicit threshold supplies a sharp predicate for this calculation; it does not resolve a sorites paradox or model vagueness.
- 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.