Obversion Immediate Inference Transformer (change quality + complement)

Obvert a categorical proposition by changing its quality and complementing its predicate.

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. Obversion changes affirmative to negative or vice versa while complementing the predicate, preserving the proposition’s meaning.^[1]

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

When to use Obversion Immediate Inference Transformer (change quality + complement)

Use this for the following task: Obvert a categorical proposition by changing its quality and complementing its predicate. Prepare the specified logical encoding before running the check or transformation.

How to use Obversion Immediate Inference Transformer (change quality + complement) 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, predicateComplemented according to the field table, then run the tool.
Read kind, subject, predicate, predicateComplemented. 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
predicateComplemented	Input predicate complemented	boolean	Required

Supply kind, subject and predicate identifiers, plus a flag recording whether the predicate is already complemented. Preserve the two identifiers, switch kind and invert that flag.

A↔E; I↔O; toggle predicateComplemented

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

Output field	Meaning	Value type
kind	Obverted proposition kind	string
subject	Subject	string
predicate	Predicate	string
predicateComplemented	Output predicate complemented	boolean

json

{
  "input": {
    "kind": "A",
    "subject": "S",
    "predicate": "P",
    "predicateComplemented": false
  },
  "output": {
    "kind": "E",
    "subject": "S",
    "predicate": "P",
    "predicateComplemented": 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. A complement is a flag here rather than a parsed set expression.

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 Contraposition Immediate Inference Full Transform Validator (A,O valid) for the complementary operation: Form full contraposition by swapping and complementing both categorical terms and test its validity.

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.
Contraposition Immediate Inference Full Transform Validator (A,O valid)
Form full contraposition by swapping and complementing both categorical terms and test its validity.