Celarent EAE-1 Valid Form Lookup
Check Celarent (EAE-1) under explicit nonempty-term assumptions using classical categorical semantics.
Description
Celarent is the categorical form EAE-1.
Celarent is the categorical form EAE-1. Its premises state that no M members belong to the P class and all S members belong to the M class; its conclusion states that no S members belong 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 Celarent EAE-1 Valid Form Lookup
Use this for the following task: Check Celarent (EAE-1) under explicit nonempty-term assumptions using classical categorical semantics. Prepare the specified logical encoding before running the check or transformation.
How to use Celarent EAE-1 Valid Form 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.
EAE-1; no extra nonempty-class assumption is required 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": []
},
"output": {
"syllogism": "EAE-1",
"valid": true,
"requiredNonemptyTerm": "none"
}
}Limitations and assumptions
The mood and figure are fixed by this tool; nonemptyTerms supplies assumptions rather than facts inferred from language. Universal classes may be empty unless the input constrains them. 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.