Hypothetical Syllogism Chain Validator (P→Q, Q→R ⊢ P→R)
Validate a hypothetical syllogism by matching two conditional links and the claimed endpoint conditional.
Description
Hypothetical syllogism chains two conditionals through a shared middle proposition.
Hypothetical syllogism chains two conditionals through a shared middle proposition. The conclusion connects the first antecedent to the second consequent.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 Hypothetical Syllogism Chain Validator (P→Q, Q→R ⊢ P→R)
Use this for the following task: Validate a hypothetical syllogism by matching two conditional links and the claimed endpoint conditional. Prepare the specified logical encoding before running the check or transformation.
How to use Hypothetical Syllogism Chain Validator (P→Q, Q→R ⊢ P→R) 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 firstAntecedent, firstConsequent, secondAntecedent, secondConsequent, conclusionAntecedent, conclusionConsequent 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 |
|---|---|---|---|
| firstAntecedent | First Antecedent | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| firstConsequent | First Consequent | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| secondAntecedent | Second Antecedent | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| secondConsequent | Second Consequent | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| conclusionAntecedent | Conclusion Antecedent | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| conclusionConsequent | Conclusion Consequent | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
Enter both conditionals and the claimed conclusion’s two identifiers. Require firstConsequent=secondAntecedent and matching conclusion endpoints.
P→Q, Q→R ⊢ P→R 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": {
"firstAntecedent": "p",
"firstConsequent": "q",
"secondAntecedent": "q",
"secondConsequent": "r",
"conclusionAntecedent": "p",
"conclusionConsequent": "r"
},
"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.
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 Constructive Dilemma Step Validator for the complementary operation: Validate constructive dilemma by matching two conditionals, the disjunction of antecedents, and the disjunction of consequents.
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.
- Constructive Dilemma Step Validator
Validate constructive dilemma by matching two conditionals, the disjunction of antecedents, and the disjunction of consequents.