Principle of Explosion Ex Falso Quodlibet Derivation Note Generator
Explicit classical propositional contradiction/ex-falso premise screen, not validity in paraconsistent logics or truth of real-world claims.
Description
Principle of Explosion Ex Falso Quodlibet Derivation Note Generator: return classical ex falso available, goal, nonclassical logics not assumed.
The classical principle of explosion allows any conclusion to follow from a contradiction. Recognizing a contradiction in stated premises differs from constructing a complete derivation.
This tool returns classical ex falso available, goal, nonclassical logics not assumed. Use the stated units and model convention when interpreting these fields.
When to use this tool
Use this tool when the supplied inputs match the specific operation described above and you need a repeatable result under its stated convention.
- Check the supported input and output contract against an existing calculation or observation.
- Use the complete example to confirm units, selector spelling and result interpretation.
How to use the tool and how it works
- Enter every field in the input table using the stated units and the exact supported selector spelling where applicable.
- Run the tool. Correct input errors before interpreting an output.
- Read the result fields below; use accompanying flags and the stated sign, boundary or model convention when interpreting a number.
Validate the known literals and goal atom. Flag classicalExFalsoAvailable when a positive atom and its negation both occur, and echo the requested goal.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| knownLiterals | Known literals. | List of text values |
| goalAtom | Goal atom. | Text |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.classicalExFalsoAvailable | Classical ex falso available flag under the exact conditions described above. |
| result.goal | Goal; use the stated units and sign convention. |
| result.nonclassicalLogicsNotAssumed | Nonclassical logics not assumed flag under the exact conditions described above. |
{
"input": {
"knownLiterals": [
"P",
"!P"
],
"goalAtom": "Q"
},
"output": {
"result": {
"classicalExFalsoAvailable": true,
"goal": "Q",
"nonclassicalLogicsNotAssumed": true
}
}
}Limitations and assumptions
- The result assumes classical logic and does not supply a proof or apply a nonclassical consequence relation.
- Every declared field is required and unexpected fields are rejected. Numeric inputs must be finite; input errors are distinct from a valid false result or an explicitly qualified output.
- Extremely large inputs and nonfinite or excessively large outputs are rejected. List positions reported by the tool use zero-based indices unless stated otherwise.
Alternative or Complementary methods
Check the underlying observations, units and conventions independently before using the result in a larger workflow. The tools listed below address nearby tasks; compare their inputs and scope before substituting one for this operation.
References
Similar or alternative tools
- a proposition classifier
Categorical propositions use A for universal affirmative, E for universal negative, I for particular affirmative and O for particular negative.
- absorption law simplifier
Absorption removes a nested combination that adds no new truth condition to its repeated leading atom.