Description
Return symmetricOnPair=(forward===reverse) and witness=(forward!==reverse).
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 symmetricOnPair=(forward===reverse) and witness=(forward!==reverse).
When to use this tool
Use Epistemic Accessibility Symmetry Pair 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 forward, reverse. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read symmetricOnPair, witness. Inspect symmetricOnPair, witness before interpreting the associated values.
Return symmetricOnPair=(forward===reverse) and witness=(forward!==reverse).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| forward | Forward | Required. Boolean. |
| reverse | Reverse | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| symmetricOnPair | Symmetric On Pair | Required. Boolean. |
| witness | Witness | Required. Boolean. |
{
"input": {
"forward": true,
"reverse": false
},
"output": {
"symmetricOnPair": false,
"witness": true
}
}Limitations and assumptions
- Two absent edges pass the pair test. Symmetry on one queried pair does not establish a globally symmetric epistemic accessibility relation or an agent's knowledge state.
- 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.
- Alpha Equivalence Bound Variable Pair
Compare flat single-binder token bodies, rejecting potential free-variable capture; nested binders are outside this model.