Simplification Rule Step Validator (P∧Q ⊢ P)
Validate conjunction elimination when the claimed conclusion is one of the premise conjunction operands.
Description
Conjunction elimination allows either component of an affirmed conjunction to be asserted.
Conjunction elimination allows either component of an affirmed conjunction to be asserted. It does not require both component identifiers to be distinct.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 Simplification Rule Step Validator (P∧Q ⊢ P)
Use this for the following task: Validate conjunction elimination when the claimed conclusion is one of the premise conjunction operands. Prepare the specified logical encoding before running the check or transformation.
How to use Simplification Rule Step Validator (P∧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 premiseLeft, premiseRight, conclusion 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 |
|---|---|---|---|
| premiseLeft | Premise Left | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| premiseRight | Premise Right | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| conclusion | Conclusion | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
Supply the two conjunction operand identifiers and the proposed conclusion identifier. Return matchesRule when the conclusion equals either operand.
from P AND Q infer P or infer 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": {
"premiseLeft": "p",
"premiseRight": "q",
"conclusion": "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 Conjunction Introduction Step Validator (P,Q ⊢ P∧Q) when you need its operation: Validate conjunction introduction by matching its two affirmed identifier premises with the claimed conjunction. 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
- Conjunction Introduction Step Validator (P,Q ⊢ P∧Q)
Validate conjunction introduction by matching its two affirmed identifier premises with the claimed conjunction.
- Addition Rule Step Validator (P ⊢ P∨Q)
Validate disjunction introduction when the affirmed premise is one of the claimed disjunction operands.