Inverse Statement Generator with Validity Warning
Generate a conditional inverse and determine whether it is equivalent for the supplied identifier atoms.
Description
The inverse of P→Q is NOT P→NOT Q.
The inverse of P→Q is NOT P→NOT Q. It generally has a different truth table, even though its wording may resemble the original conditional.1
The tool returns original, inverse, equivalent. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Inverse Statement Generator with Validity Warning
Use this for the following task: Generate a conditional inverse and determine whether it is equivalent for the supplied identifier atoms. Prepare the specified logical encoding before running the check or transformation.
How to use Inverse Statement Generator with Validity Warning 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 antecedent, consequent according to the field table, then run the tool.
- Read original, inverse, 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 |
|---|---|---|---|
| antecedent | Antecedent | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| consequent | Consequent | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
Supply the two conditional identifiers. Render the original and inverse, and set equivalent only when the identifiers are exactly the same.
inverse = NOT P→NOT Q; equivalent flag = identical atom identifiers The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| original | Original conditional | string (propositional-formula) |
| inverse | Inverse conditional | string (propositional-formula) |
| equivalent | Logically equivalent | boolean |
{
"input": {
"antecedent": "p",
"consequent": "q"
},
"output": {
"original": "(p -> q)",
"inverse": "(!p -> !q)",
"equivalent": false
}
}Limitations and assumptions
Operands are case-sensitive identifier atoms, not complete expressions. The tool does not parse a proof or determine whether the premises are true. Distinct identifiers are treated as independent atoms; external equivalences are not inferred.
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 Converse Statement Generator with Validity Warning when you need its operation: Generate a conditional converse and determine whether it is equivalent for the supplied identifier atoms. Choose Contrapositive Form Generator (P→Q ≡ ¬Q→¬P) for the complementary operation: Generate the equivalent contrapositive of a conditional between identifier atoms.
Background reference: Additional rules for TFL.
References
-
Additional rules for TFL — forallx Calgary, Open Logic Project
Similar or alternative tools
- Converse Statement Generator with Validity Warning
Generate a conditional converse and determine whether it is equivalent for the supplied identifier atoms.
- Contrapositive Form Generator (P→Q ≡ ¬Q→¬P)
Generate the equivalent contrapositive of a conditional between identifier atoms.