Bramantip AAI-4 Fourth Figure Valid Lookup
Check Bramantip (AAI-4) under explicit nonempty-term assumptions using classical categorical semantics.
Description
Bramantip is the categorical form AAI-4.
Bramantip is the categorical form AAI-4. Its premises state that all P members belong to the M class and all M members belong to the S class; its conclusion states that some S member belongs to the P class. S is the conclusion’s subject, P its predicate and M the middle term.1
The tool returns syllogism, valid, requiredNonemptyTerm. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Bramantip AAI-4 Fourth Figure Valid Lookup
Use this for the following task: Check Bramantip (AAI-4) under explicit nonempty-term assumptions using classical categorical semantics. Prepare the specified logical encoding before running the check or transformation.
How to use Bramantip AAI-4 Fourth Figure Valid Lookup 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 nonemptyTerms according to the field table, then run the tool.
- Read syllogism, valid, requiredNonemptyTerm. 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 |
|---|---|---|---|
| nonemptyTerms | Terms assumed nonempty | list of string; minimum entries 0; maximum entries 3; each entry: choices "S", "M", "P" | Required |
Supply the class identifiers S, M or P whose nonemptiness is assumed, or an empty list for none. Enumerate the 255 nonempty occupancy patterns of the eight S/M/P regions; discard patterns violating those assumptions and look for true premises with a false conclusion. Return valid if no counterexample remains.
AAI-4; validity requires nonempty P The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| syllogism | Mood and figure | string |
| valid | Valid under supplied existence assumptions | boolean |
| requiredNonemptyTerm | Required existence assumption | string |
{
"input": {
"nonemptyTerms": [
"P"
]
},
"output": {
"syllogism": "AAI-4",
"valid": true,
"requiredNonemptyTerm": "P"
}
}Limitations and assumptions
The mood and figure are fixed by this tool; nonemptyTerms supplies assumptions rather than facts inferred from language. This form fails without an appropriate nonemptiness assumption; requiredNonemptyTerm reports P. No concrete counterexample or proof text is returned.
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 Categorical Syllogism Mood-Figure Label Parser (EAE-1 etc.) when you need its operation: Parse a categorical mood and figure such as AAA-1 into proposition kinds and standard S, M, and P term positions. Choose Existential Import Modern Invalidity Flag for AA-3 for the complementary operation: Identify categorical syllogisms that become valid only when nonempty terms are assumed.
Background reference: Categorical Logic.
References
-
Categorical Logic — Philip B. Stark, University of California Berkeley
Similar or alternative tools
- Categorical Syllogism Mood-Figure Label Parser (EAE-1 etc.)
Parse a categorical mood and figure such as AAA-1 into proposition kinds and standard S, M, and P term positions.
- Existential Import Modern Invalidity Flag for AA-3
Identify categorical syllogisms that become valid only when nonempty terms are assumed.