Description
Evaluate box and diamond on an explicit finite list of accessible successor truth values.
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.
Evaluate box and diamond on an explicit finite list of accessible successor truth values.
When to use this tool
Use Modal Box Vacuous Successor Case 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 successorValues. 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, vacuous. Inspect box, diamond, vacuous before interpreting the associated values.
Return box=every successorValue, diamond=some successorValue, and vacuous when the list is empty.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| successorValues | Successor Values | Required. Array of boolean; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| box | Box | Required. Boolean. |
| diamond | Diamond | Required. Boolean. |
| vacuous | Vacuous | Required. Boolean. |
{
"input": {
"successorValues": []
},
"output": {
"box": true,
"diamond": false,
"vacuous": true
}
}Limitations and assumptions
- With no successors box is true and diamond false. This evaluates supplied successor truth values for one world and does not construct an accessibility relation or prove a modal formula globally.
- 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.
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 Successor Count Budget
Finite modal truth from supplied successor counts, with vacuous necessity at zero successors.
- Exclusive OR Three Valued Unknown Case
Strong Kleene exclusive-or: an unknown operand gives unknown.