Description
Return missingLoops for worlds lacking a self-edge and reflexive when no loop is missing.
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.
Return missingLoops for worlds lacking a self-edge and reflexive when no loop is missing.
When to use this tool
Use Possible World One Relation Reflexivity 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 worlds, edgeSources, edgeTargets. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read missingLoops, reflexive. Inspect reflexive before interpreting the associated values.
Require distinct worlds and equally sized edgeSources and edgeTargets whose tokens belong to worlds. Return missingLoops for worlds lacking a self-edge and reflexive when no loop is missing.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| worlds | Worlds | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| edgeSources | Edge Sources | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| edgeTargets | Edge Targets | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| missingLoops | Missing Loops | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| reflexive | Reflexive | Required. Boolean. |
{
"input": {
"worlds": [
"a",
"b"
],
"edgeSources": [
"a",
"b"
],
"edgeTargets": [
"a",
"b"
]
},
"output": {
"missingLoops": [],
"reflexive": true
}
}Limitations and assumptions
- Duplicate edges are allowed. An empty domain is reflexive by vacuity; the tool checks only relation reflexivity, not modal frame validity or other accessibility properties.
- 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 Accessibility Edge Flag
Inspect explicitly listed directed accessibility edges without assuming modal frame axioms.
- Epistemic Accessibility Symmetry Pair
Return symmetricOnPair=(forward===reverse) and witness=(forward!==reverse).