Description
Compute Fréchet lower max(0,p+q-1) and upper min(p,q), their signed conjunction slacks and inclusive coherence.
Evidence weights and credences are numerical representations under a chosen model. Likelihood ratios, probabilities, logarithmic weights and confidence bounds have different meanings; one local calculation does not establish the truth of a claim.
Compute Fréchet lower max(0,p+q-1) and upper min(p,q), their signed conjunction slacks and inclusive coherence.
When to use this tool
Use Belief Consistency Probability Bound Gap when you need an explicit evidence-weight or probability-consistency term.
How to use the tool and how it works
- Enter firstProbability, secondProbability, conjunction. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read frechetLower, frechetUpper, lowerSlack, upperSlack, coherent. Inspect coherent before interpreting the associated values.
Require marginal/conjunction probabilities in [0, 1]. Compute Fréchet lower max(0,p+q-1) and upper min(p,q), their signed conjunction slacks and inclusive coherence.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstProbability | First Probability | Required. Finite number; minimum 0; maximum 1. |
| secondProbability | Second Probability | Required. Finite number; minimum 0; maximum 1. |
| conjunction | Conjunction | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| frechetLower | Frechet Lower | Required. Finite number. |
| frechetUpper | Frechet Upper | Required. Finite number. |
| lowerSlack | Lower Slack | Required. Finite number. |
| upperSlack | Upper Slack | Required. Finite number. |
| coherent | Coherent | Required. Boolean. |
{
"input": {
"firstProbability": 0.6,
"secondProbability": 0.7,
"conjunction": 0.4
},
"output": {
"frechetLower": 0.2999999999999998,
"frechetUpper": 0.6,
"lowerSlack": 0.1000000000000002,
"upperSlack": 0.19999999999999996,
"coherent": true
}
}Limitations and assumptions
- An incoherent conjunction is returned with false rather than rejected. This checks one probability pair, not a complete coherent belief system or actual hypothesis truth.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Evaluate source quality and the complete inference model. Check likelihood meaning, dependence, prior assumptions, normalization and uncertainty rather than substituting counts or weights for justified evidence.
References
Similar or alternative tools
- Prior Credence Rounding Envelope
Return reported±halfwidth clipped to [0, 1].
- Assertion Confidence Interval Width
Return upper-minus-lower width and arithmetic midpoint.