Logical Contradiction Pair Opposed-Rows Detector
Check whether two complete truth columns are exact negations in the same valuation order.
Description
Two truth-table columns are contradictory when exactly one is true under every assignment.
Two truth-table columns are contradictory when exactly one is true under every assignment. This is a rowwise complement relation, stronger than merely differing somewhere.1
The tool returns opposed. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Logical Contradiction Pair Opposed-Rows Detector
Use this for the following task: Check whether two complete truth columns are exact negations in the same valuation order. Prepare the specified logical encoding before running the check or transformation.
How to use Logical Contradiction Pair Opposed-Rows Detector 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 left, right according to the field table, then run the tool.
- Read opposed. 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 |
|---|---|---|---|
| left | Left truth column | list of boolean; minimum entries 1; maximum entries 4096 | Required |
| right | Right truth column | list of boolean; minimum entries 1; maximum entries 4096 | Required |
Provide two equally sized Boolean columns representing complete tables. Require a positive power-of-two length and compare every pair of rows.
opposed ⇔ every left[row] differs from right[row] The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| opposed | Opposed | boolean |
{
"input": {
"left": [
false,
true
],
"right": [
true,
false
]
},
"output": {
"opposed": 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 Logical Equivalence Biconditional Row Match Checker when you need its operation: Test logical equivalence of two complete truth columns with the same valuation order. Choose Contradiction All-Rows-False Checker for the complementary operation: Check whether every row in a complete ordered Boolean truth column is false.
Background reference: Complete truth tables.
References
-
Complete truth tables — forallx Calgary, Open Logic Project
Similar or alternative tools
- Logical Equivalence Biconditional Row Match Checker
Test logical equivalence of two complete truth columns with the same valuation order.
- Contradiction All-Rows-False Checker
Check whether every row in a complete ordered Boolean truth column is false.