Law of Non-Contradiction Violation Detector (P∧¬P)
Find exact P and !P pairs in explicit classical literal inventory; no natural-language contradiction detection or SAT solving.
Description
Law of Non-Contradiction Violation Detector (P∧¬P): return contradictory atom ids, explicit contradiction present.
In classical propositional notation, an atom and its negation cannot both be true in the same interpretation. An explicit literal list allows that narrow conflict to be checked directly.
This tool returns contradictory atom ids, explicit contradiction present. 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 each uppercase atom, optionally preceded by one !. Find positive atoms whose !-prefixed counterpart is present, remove duplicates and sort the conflicting atom IDs.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| declaredLiterals | Declared literals. | List of text values |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.contradictoryAtomIds | Contradictory atom ids list, in the ordering described in the calculation. |
| result.explicitContradictionPresent | Explicit contradiction present flag under the exact conditions described above. |
{
"input": {
"declaredLiterals": [
"P",
"!P",
"Q"
]
},
"output": {
"result": {
"contradictoryAtomIds": [
"P"
],
"explicitContradictionPresent": true
}
}
}Limitations and assumptions
- The tool finds explicit literal pairs; it does not infer hidden contradictions from arbitrary formulas.
- 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
- contradiction pair opposed detector
Two truth-table columns are contradictory when exactly one is true under every assignment.
- four term equivocation detector
A categorical syllogism connects exactly three term meanings.