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.
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. Subalternation carries truth from a universal statement to its corresponding particular statement when the subject class exists.1
The tool returns subaltern, implicationGuaranteed. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Square of Opposition Subaltern Implication Mapper (A-I, E-O)
Use this for the following task: Map A to I or E to O and state whether a nonempty subject guarantees universal-to-particular implication. Prepare the specified logical encoding before running the check or transformation.
How to use Square of Opposition Subaltern Implication Mapper (A-I, E-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 subaltern, implicationGuaranteed. 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 | Universal proposition kind | string; choices "A", "E" | Required |
| subjectNonempty | Subject class known nonempty | boolean | Required |
Choose A or E and provide subjectNonempty. Return the matching particular kind and whether the nonemptiness assumption supports that implication.
A → I; E → O; implicationGuaranteed = subjectNonempty The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| subaltern | Particular proposition kind | string |
| implicationGuaranteed | Universal implies particular under the assumption | boolean |
{
"input": {
"kind": "A",
"subjectNonempty": true
},
"output": {
"subaltern": "I",
"implicationGuaranteed": true
}
}Limitations and assumptions
The converse implication is not established. No class existence or actual proposition truth is checked.
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 Subcontrary Pair Mapper (I-O) when you need its operation: Map an I or O proposition to its subcontrary and state whether a nonempty subject guarantees the relation. Choose Square of Opposition Contrary Pair Mapper (A-E) for the complementary operation: Map an A or E proposition to its contrary and state whether a nonempty subject guarantees the relation.
Background reference: Categorical Logic.
References
-
Categorical Logic — Philip B. Stark, University of California Berkeley
Similar or alternative tools
- 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.
- Square of Opposition Contrary Pair Mapper (A-E)
Map an A or E proposition to its contrary and state whether a nonempty subject guarantees the relation.