Contraposition Immediate Inference Full Transform Validator (A,O valid)

Form full contraposition by swapping and complementing both categorical terms and test its validity.

Description

Categorical propositions use A for universal affirmative, E for universal negative, I for particular affirmative and O for particular negative.

Categorical propositions use A for universal affirmative, E for universal negative, I for particular affirmative and O for particular negative. Full categorical contraposition swaps subject and predicate and complements both classes. It preserves A and O propositions under the standard form rules.^[1]

The tool returns kind, subject, predicate, subjectComplemented, predicateComplemented, valid. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.

When to use Contraposition Immediate Inference Full Transform Validator (A,O valid)

Use this for the following task: Form full contraposition by swapping and complementing both categorical terms and test its validity. Prepare the specified logical encoding before running the check or transformation.

How to use Contraposition Immediate Inference Full Transform Validator (A,O valid) 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 kind, subject, predicate according to the field table, then run the tool.
Read kind, subject, predicate, subjectComplemented, predicateComplemented, valid. 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
kind	Proposition kind	string; choices "A", "E", "I", "O"	Required
subject	Subject	string; maximum text length 100; pattern ^(?!(?:true\|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S])	Required
predicate	Predicate	string; maximum text length 100; pattern ^(?!(?:true\|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S])	Required

Supply kind and uncomplemented term identifiers. Return the swapped identifiers, both complement flags set true, and the kind-based validity flag.

swap S/P, complement both; valid = kind is A or O

The symbols and boundary conditions refer to the supplied fields and the implementation described above.

Output field	Meaning	Value type
kind	Contraposed proposition kind	string
subject	Subject	string
predicate	Predicate	string
subjectComplemented	Output subject complemented	boolean
predicateComplemented	Output predicate complemented	boolean
valid	Full contraposition preserves truth	boolean

json

{
  "input": {
    "kind": "A",
    "subject": "S",
    "predicate": "P"
  },
  "output": {
    "kind": "A",
    "subject": "P",
    "predicate": "S",
    "subjectComplemented": true,
    "predicateComplemented": true,
    "valid": true
  }
}

Limitations and assumptions

The implementation uses the standard kind rule for all identifier pairs and returns false for E or I. It does not test special class relationships or conversion by limitation.

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 Conversion Immediate Inference Subject-Predicate Swapper (E,I valid) when you need its operation: Swap subject and predicate by simple conversion and test whether that conversion preserves truth for identifier categories. Choose Obversion Immediate Inference Transformer (change quality + complement) for the complementary operation: Obvert a categorical proposition by changing its quality and complementing its predicate.

Background reference: Categorical Logic.

References

Categorical Logic — Philip B. Stark, University of California Berkeley

Similar or alternative tools

Conversion Immediate Inference Subject-Predicate Swapper (E,I valid)
Swap subject and predicate by simple conversion and test whether that conversion preserves truth for identifier categories.
Obversion Immediate Inference Transformer (change quality + complement)
Obvert a categorical proposition by changing its quality and complementing its predicate.