Contrapositive Form Generator (P→Q ≡ ¬Q→¬P)
Generate the equivalent contrapositive of a conditional between identifier atoms.
Description
A conditional and its contrapositive share the same truth table in classical logic.
A conditional and its contrapositive share the same truth table in classical logic. Contraposition reverses the direction and negates both operands.1
The tool returns original, rewritten. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Contrapositive Form Generator (P→Q ≡ ¬Q→¬P)
Use this for the following task: Generate the equivalent contrapositive of a conditional between identifier atoms. Prepare the specified logical encoding before running the check or transformation.
How to use Contrapositive Form Generator (P→Q ≡ ¬Q→¬P) 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, rewritten. 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 antecedent and consequent identifiers. Render the original conditional and the negated reversed form.
P→Q ≡ NOT Q→NOT P The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| original | Original propositional formula | string (propositional-formula) |
| rewritten | Equivalent propositional formula | string (propositional-formula) |
{
"input": {
"antecedent": "p",
"consequent": "q"
},
"output": {
"original": "(p -> q)",
"rewritten": "(!q -> !p)"
}
}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.
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 Modus Tollens Inference Step Validator (P→Q, ¬Q ⊢ ¬P) for the complementary operation: Validate a modus tollens step by matching the identifiers negated in its premise and conclusion.
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.
- Modus Tollens Inference Step Validator (P→Q, ¬Q ⊢ ¬P)
Validate a modus tollens step by matching the identifiers negated in its premise and conclusion.