Logical Equivalence Biconditional Row Match Checker
Test logical equivalence of two complete truth columns with the same valuation order.
Description
Logical equivalence means two formulas agree under every assignment.
Logical equivalence means two formulas agree under every assignment. Matching complete truth-table columns lets their supplied truth values be compared row by row.1
The tool returns equivalent. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Logical Equivalence Biconditional Row Match Checker
Use this for the following task: Test logical equivalence of two complete truth columns with the same valuation order. Prepare the specified logical encoding before running the check or transformation.
How to use Logical Equivalence Biconditional Row Match 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 left, right according to the field table, then run the tool.
- Read equivalent. 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 equal-length Boolean columns of positive power-of-two length, each at most 4096 rows. Compare corresponding values and return a single flag.
equivalent ⇔ every left[row] equals right[row] The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| equivalent | Equivalent | boolean |
{
"input": {
"left": [
false,
true
],
"right": [
false,
true
]
},
"output": {
"equivalent": 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 Contradiction Pair Opposed-Rows Detector when you need its operation: Check whether two complete truth columns are exact negations in the same valuation order. 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
- Logical Contradiction Pair Opposed-Rows Detector
Check whether two complete truth columns are exact negations in the same valuation order.
- Tautology All-Rows-True Checker
Check whether every row in a complete ordered Boolean truth column is true.