Contradiction All-Rows-False Checker
Check whether every row in a complete ordered Boolean truth column is false.
Description
A contradiction is false under every assignment of its variables.
A contradiction is false under every assignment of its variables. A complete supplied truth column can establish that classification for the represented formula.1
The tool returns contradiction. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Contradiction All-Rows-False Checker
Use this for the following task: Check whether every row in a complete ordered Boolean truth column is false. Prepare the specified logical encoding before running the check or transformation.
How to use Contradiction All-Rows-False Checker and understand its results
- Prepare the requested Boolean values, complete truth-table rows, or identifier atoms. An atom is a name such as p or premise_1, not a natural-language sentence.
- Enter values according to the field table, then run the tool.
- Read contradiction. Use the matching rule, assignment order or nonempty-class assumptions below to interpret the result.
- For a false check, inspect the supplied encoding and matching rule. A well-formed false result is different from an input error.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| values | Complete truth column | list of boolean; minimum entries 1; maximum entries 4096 | Required |
Supply 1..4096 Boolean rows with a power-of-two length. Validate the table shape and test whether every row is false.
contradiction ⇔ every value is false The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| contradiction | Contradiction | boolean |
{
"input": {
"values": [
false,
false
]
},
"output": {
"contradiction": true
}
}Limitations and assumptions
Supply a complete table in a consistent assignment order. The tool evaluates the supplied rows rather than parsing a formula or verifying the correctness of the table.
The supplied encodings must represent the intended propositions or classes. No natural-language parsing or assessment of empirical premise truth is performed. Malformed input gives a tool error rather than a logical false result.
Alternative or Complementary methods
Choose Contingency Mixed-Outcome Classifier when you need its operation: Classify a complete ordered Boolean truth column as a tautology, contradiction, or contingency. Choose Tautology All-Rows-True Checker for the complementary operation: Check whether every row in a complete ordered Boolean truth column is true.
Background reference: Complete truth tables.
References
-
Complete truth tables — forallx Calgary, Open Logic Project
Similar or alternative tools
- Contingency Mixed-Outcome Classifier
Classify a complete ordered Boolean truth column as a tautology, contradiction, or contingency.
- Tautology All-Rows-True Checker
Check whether every row in a complete ordered Boolean truth column is true.