Addition Rule Step Validator (P ⊢ P∨Q)
Validate disjunction introduction when the affirmed premise is one of the claimed disjunction operands.
Description
Disjunction introduction adds another possible disjunct to an affirmed premise.
Disjunction introduction adds another possible disjunct to an affirmed premise. Inclusive OR remains true whenever either operand is already true.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 Addition Rule Step Validator (P ⊢ P∨Q)
Use this for the following task: Validate disjunction introduction when the affirmed premise is one of the claimed disjunction operands. Prepare the specified logical encoding before running the check or transformation.
How to use Addition Rule Step Validator (P ⊢ 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 premise, 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 |
|---|---|---|---|
| premise | 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 affirmed identifier and the two claimed disjunction operands. Return matchesRule when either operand equals the premise.
P ⊢ P OR Q or Q OR 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": {
"premise": "p",
"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 Conjunction Introduction Step Validator (P,Q ⊢ P∧Q) for the complementary operation: Validate conjunction introduction by matching its two affirmed identifier premises with the claimed conjunction.
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.
- Conjunction Introduction Step Validator (P,Q ⊢ P∧Q)
Validate conjunction introduction by matching its two affirmed identifier premises with the claimed conjunction.