Modus Tollens Inference Step Validator (P→Q, ¬Q ⊢ ¬P)
Validate a modus tollens step by matching the identifiers negated in its premise and conclusion.
Description
Modus tollens infers a negated antecedent from a conditional and denial of its consequent.
Modus tollens infers a negated antecedent from a conditional and denial of its consequent. Negation belongs to the designated premise and conclusion fields.1
The tool returns matchesRule. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Modus Tollens Inference Step Validator (P→Q, ¬Q ⊢ ¬P)
Use this for the following task: Validate a modus tollens step by matching the identifiers negated in its premise and conclusion. Prepare the specified logical encoding before running the check or transformation.
How to use Modus Tollens Inference Step Validator (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, negatedPremise, negatedConclusion according to the field table, then run the tool.
- Read matchesRule. 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 |
| negatedPremise | Negated Premise | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| negatedConclusion | Negated Conclusion | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
Enter antecedent and consequent identifiers, then the atom being negated in the premise and conclusion. Match the negated premise to Q and negated conclusion to P.
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 |
|---|---|---|
| matchesRule | Matches Rule | boolean |
{
"input": {
"antecedent": "p",
"consequent": "q",
"negatedPremise": "q",
"negatedConclusion": "p"
},
"output": {
"matchesRule": true
}
}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. Enter q rather than !q in a negated field.
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 Modus Ponens Inference Step Validator (P→Q, P ⊢ Q) when you need its operation: Validate a modus ponens step using identifier operands for its conditional, affirmed premise, and claimed conclusion. Choose Denying the Antecedent Fallacy Flag Detector for the complementary operation: Detect the denying-the-antecedent pattern with distinct identifier atoms and explicitly negated terms.
Background reference: Additional rules for TFL.
References
-
Additional rules for TFL — forallx Calgary, Open Logic Project
Similar or alternative tools
- Modus Ponens Inference Step Validator (P→Q, P ⊢ Q)
Validate a modus ponens step using identifier operands for its conditional, affirmed premise, and claimed conclusion.
- Denying the Antecedent Fallacy Flag Detector
Detect the denying-the-antecedent pattern with distinct identifier atoms and explicitly negated terms.