Disjunctive Syllogism Validator (P∨Q, ¬P ⊢ Q)
Validate disjunctive syllogism by matching a disjunction, a negated operand, and the remaining conclusion atom.
Description
Disjunctive syllogism infers the surviving disjunct after the other disjunct is denied.
Disjunctive syllogism infers the surviving disjunct after the other disjunct is denied. Inclusive disjunction is sufficient for this inference.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 Disjunctive Syllogism Validator (P∨Q, ¬P ⊢ Q)
Use this for the following task: Validate disjunctive syllogism by matching a disjunction, a negated operand, and the remaining conclusion atom. Prepare the specified logical encoding before running the check or transformation.
How to use Disjunctive Syllogism 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 left, right, negatedPremise, 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 |
|---|---|---|---|
| left | Left | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| right | Right | 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 |
| conclusion | Conclusion | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
Supply the two disjunct identifiers, the atom denied and the claimed conclusion. Accept either side’s denial when the conclusion matches the other side.
P OR Q, NOT P ⊢ Q; or NOT Q ⊢ 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": {
"left": "p",
"right": "q",
"negatedPremise": "p",
"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 negatedPremise field contains the atom, without a ! prefix.
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 Simplification Rule Step Validator (P∧Q ⊢ P) for the complementary operation: Validate conjunction elimination when the claimed conclusion is one of the premise conjunction operands.
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.
- Simplification Rule Step Validator (P∧Q ⊢ P)
Validate conjunction elimination when the claimed conclusion is one of the premise conjunction operands.