Description
Finite modal truth from supplied successor counts, with vacuous necessity at zero successors.
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 modal truth from supplied successor counts, with vacuous necessity at zero successors.
When to use this tool
Use Modal Successor Count Budget 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 successors, satisfying. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read box, diamond, counterexamples. Inspect box, diamond before interpreting the associated values.
Require nonnegative integer successors and satisfying within zero through successors. Return box=(satisfying===successors), diamond=(satisfying>0), and counterexamples=successors-satisfying.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| successors | Successors | Required. Safe integer; minimum 0. |
| satisfying | Satisfying | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| box | Box | Required. Boolean. |
| diamond | Diamond | Required. Boolean. |
| counterexamples | Counterexamples | Required. Safe integer. |
{
"input": {
"successors": 0,
"satisfying": 0
},
"output": {
"box": true,
"diamond": false,
"counterexamples": 0
}
}Limitations and assumptions
- The counts summarize one world's successors under one predicate. With no successors box is true and diamond false; the underlying graph and truth assignments are not verified.
- 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
- Modal Box Vacuous Successor Case
Evaluate box and diamond on an explicit finite list of accessible successor truth values.
- Argument Conclusion Reference Count
Count exact supplied conclusion references without deciding logical entailment.