Finite Relation Partial Order Property Report
Report partial-order property evidence for an explicit finite relation; does not assume a claimed order or repair missing pairs.
Description
Report partial-order property evidence for an explicit finite relation; does not assume a claimed order or repair missing pairs.
A partial order must be reflexive, antisymmetric and transitive on its declared universe.
When to use this tool
Report partial-order property evidence for an explicit finite relation; does not assume a claimed order or repair missing pairs.
- Prepare the supplied pairsJson, universe fields for this operation.
- Compare the complete example with the representation used by your own input before carrying the result into another step.
How to use the tool and how it works
- Enter pairsJson, universe. Use the exact text syntax, units and index conventions explained below.
- Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
- Read result.properties, result.holds. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Deduplicate valid in-universe pairs and compute reflexive, symmetric, antisymmetric and transitive flags. holds is the conjunction of reflexive, antisymmetric and transitive.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| pairsJson | JSON text, entered as one text field. The decoded structure is illustrated below; it is not a separate file. | Text |
| universe | universe. | List of strings; at most 128 entries |
For the JSON text fields, the following decoded structures show the example records before they are serialized into input strings. Keep field names, list nesting and value types as shown.
[
{
"field": "pairsJson",
"decoded": [
[
"a",
"b"
],
[
"b",
"a"
]
]
}
]| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.properties | The properties value under the stated formula or text convention. |
| result.holds | True exactly when the stated property passes; it does not establish other properties. |
{
"input": {
"pairsJson": "[[\"a\",\"b\"],[\"b\",\"a\"]]",
"universe": [
"a",
"b"
]
},
"output": {
"result": {
"properties": {
"reflexive": false,
"symmetric": true,
"antisymmetric": false,
"transitive": false
},
"holds": false
}
}
}Limitations and assumptions
- The universe must have unique string labels. No closure is assumed, and symmetric is reported for context rather than required for a partial order.
- All declared input fields are required and unexpected top-level fields are rejected. Numbers must be finite; lists are limited to 128 entries and ordinary text fields to 8,192 UTF-16 code units, with tighter limits where stated.
- JSON text inputs must parse within bounded nesting and size limits. Numeric outputs outside the safe finite range are rejected; large exact integer results use decimal strings. Indexes and half-open spans are zero-based unless a rank is explicitly described as one-based.
Alternative or Complementary methods
Declare the full universe and distinguish testing a property from adding its closure. Use separate functionality and totality checks before interpreting a relation as a function.
References
Similar or alternative tools
- Finite Relation Equivalence Property Report
Report equivalence property evidence for an explicit finite relation; does not assume a claimed order or repair missing pairs.
- Finite Relation Minimal Maximal Elements
Return all minimal and maximal elements only after validating a supplied finite partial order; these need not be a unique least/greatest element.