Conjunction Introduction Step Validator (P,Q ⊢ P∧Q)
Validate conjunction introduction by matching its two affirmed identifier premises with the claimed conjunction.
Description
Conjunction introduction joins two affirmed premises.
Conjunction introduction joins two affirmed premises. Either ordering of those premises is accepted for the proposed conjunction.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 Conjunction Introduction Step Validator (P,Q ⊢ P∧Q)
Use this for the following task: Validate conjunction introduction by matching its two affirmed identifier premises with the claimed conjunction. Prepare the specified logical encoding before running the check or transformation.
How to use Conjunction Introduction Step Validator (P,Q ⊢ P∧Q) 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 firstPremise, secondPremise, conclusionLeft, conclusionRight 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 |
|---|---|---|---|
| firstPremise | First Premise | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| secondPremise | Second Premise | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| conclusionLeft | Conclusion Left | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| conclusionRight | Conclusion Right | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
Supply the two premise identifiers and claimed conjunction’s left and right identifiers. Match the two pairs in their original or reversed order.
P, Q ⊢ P AND Q 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": {
"firstPremise": "p",
"secondPremise": "q",
"conclusionLeft": "p",
"conclusionRight": "q"
},
"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 Simplification Rule Step Validator (P∧Q ⊢ P) when you need its operation: Validate conjunction elimination when the claimed conclusion is one of the premise conjunction operands. Choose Addition Rule Step Validator (P ⊢ P∨Q) for the complementary operation: Validate disjunction introduction when the affirmed premise is one of the claimed disjunction operands.
Background reference: Additional rules for TFL.
References
-
Additional rules for TFL — forallx Calgary, Open Logic Project
Similar or alternative tools
- Simplification Rule Step Validator (P∧Q ⊢ P)
Validate conjunction elimination when the claimed conclusion is one of the premise conjunction operands.
- Addition Rule Step Validator (P ⊢ P∨Q)
Validate disjunction introduction when the affirmed premise is one of the claimed disjunction operands.