Square of Opposition Subcontrary Pair Mapper (I-O)
Map an I or O proposition to its subcontrary and state whether a nonempty subject guarantees the relation.
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. Subcontraries I and O may both be true but cannot both be false when their common subject class exists.1
The tool returns subcontrary, relationGuaranteed. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Square of Opposition Subcontrary Pair Mapper (I-O)
Use this for the following task: Map an I or O proposition to its subcontrary and state whether a nonempty subject guarantees the relation. Prepare the specified logical encoding before running the check or transformation.
How to use Square of Opposition Subcontrary Pair Mapper (I-O) 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, subjectNonempty according to the field table, then run the tool.
- Read subcontrary, relationGuaranteed. 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 | Particular proposition kind | string; choices "I", "O" | Required |
| subjectNonempty | Subject class known nonempty | boolean | Required |
Choose I or O and supply whether the subject class is known nonempty. Return the opposite particular kind and the supplied existence-based guarantee.
I ↔ O; relationGuaranteed = subjectNonempty The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| subcontrary | Subcontrary proposition kind | string |
| relationGuaranteed | Cannot both be false under the assumption | boolean |
{
"input": {
"kind": "I",
"subjectNonempty": true
},
"output": {
"subcontrary": "O",
"relationGuaranteed": true
}
}Limitations and assumptions
The tool maps forms rather than evaluating particular statements. With an empty subject both particular statements are false.
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 Square of Opposition Subaltern Implication Mapper (A-I, E-O) when you need its operation: Map A to I or E to O and state whether a nonempty subject guarantees universal-to-particular implication. Choose Square of Opposition Contradictory Pair Mapper (A-O, E-I) for the complementary operation: Map a categorical proposition to its contradictory form for the same subject and predicate.
Background reference: Categorical Logic.
References
-
Categorical Logic — Philip B. Stark, University of California Berkeley
Similar or alternative tools
- Square of Opposition Subaltern Implication Mapper (A-I, E-O)
Map A to I or E to O and state whether a nonempty subject guarantees universal-to-particular implication.
- Square of Opposition Contradictory Pair Mapper (A-O, E-I)
Map a categorical proposition to its contradictory form for the same subject and predicate.