Existential Import Modern Invalidity Flag for AA-3

Identify categorical syllogisms that become valid only when nonempty terms are assumed.

Description

Some traditional categorical syllogisms reach particular conclusions only by assuming a class exists.

Some traditional categorical syllogisms reach particular conclusions only by assuming a class exists. Modern set semantics allows a subject or predicate class to be empty.^[1]

The tool returns validWithoutExistence, validWithAllTermsNonempty, existentialImportRequired. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.

When to use Existential Import Modern Invalidity Flag for AA-3

Use this for the following task: Identify categorical syllogisms that become valid only when nonempty terms are assumed. Prepare the specified logical encoding before running the check or transformation.

How to use Existential Import Modern Invalidity Flag for AA-3 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 majorKind, minorKind, conclusionKind, figure according to the field table, then run the tool.
Read validWithoutExistence, validWithAllTermsNonempty, existentialImportRequired. 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
majorKind	Major proposition kind	string; choices "A", "E", "I", "O"	Required
minorKind	Minor proposition kind	string; choices "A", "E", "I", "O"	Required
conclusionKind	Conclusion proposition kind	string; choices "A", "E", "I", "O"	Required
figure	Syllogism figure	integer; minimum 1; maximum 4	Required

Choose major, minor and conclusion kinds and the figure. Run the finite Venn-region counterexample test first without class-existence assumptions and then with all three classes required nonempty.

requiresExistentialImport = invalid with no nonemptiness assumptions AND valid when S, M and P are nonempty

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

Output field	Meaning	Value type
validWithoutExistence	Valid Without Existence	boolean
validWithAllTermsNonempty	Valid With All Terms Nonempty	boolean
existentialImportRequired	Existential Import Required	boolean

json

{
  "input": {
    "majorKind": "A",
    "minorKind": "A",
    "conclusionKind": "I",
    "figure": 3
  },
  "output": {
    "validWithoutExistence": false,
    "validWithAllTermsNonempty": true,
    "existentialImportRequired": true
  }
}

Limitations and assumptions

The output flags the need for some existential import but does not identify its weakest sufficient assumption. It is false for forms invalid even under all three assumptions.

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 Felapton EAO-3 Valid Form Lookup when you need its operation: Check Felapton (EAO-3) under explicit nonempty-term assumptions using classical categorical semantics. Choose Darapti AAI-3 Third Figure Valid Lookup for the complementary operation: Check Darapti (AAI-3) under explicit nonempty-term assumptions using classical categorical semantics.

Background reference: Categorical Logic.

References

Categorical Logic — Philip B. Stark, University of California Berkeley

Similar or alternative tools

Felapton EAO-3 Valid Form Lookup
Check Felapton (EAO-3) under explicit nonempty-term assumptions using classical categorical semantics.
Darapti AAI-3 Third Figure Valid Lookup
Check Darapti (AAI-3) under explicit nonempty-term assumptions using classical categorical semantics.