Understand the subject
What is a categorical syllogism?
A categorical syllogism uses two category statements and a conclusion in a named mood and figure.
Use it to check the valid form of a traditional A/E/I/O argument.
See the structure
What the rule checks
T T → TT F → FF T → TF F → T
mood records A/E/I/O; figure records middle-term positionWorked interpretation
Read the result in context
AAA-1, Barbara, is valid.
Interpret with care
Important boundary
This calculator uses modern Boolean logic without existential import for universal statements.
Use the Set Operations Calculator to explore small finite examples.
Quick guide
How to use this calculator
- Enter values using the notation shown beside each field.
- Choose a calculation mode when the tool offers more than one interpretation.
- Read the primary answer first, then inspect the supporting details.
Calculation method
Apply the stated definition
Mood records A/E/I/O proposition types; figure records middle-term position.
The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.
Worked example
Worked example
AAA-1 (Barbara) is valid.
Mood records A/E/I/O proposition types; figure records middle-term position.
Supported inputs
Precision and limits
Finite, bounded input
Set and logic tools use finite inputs so every result can be checked completely. Each page states its practical size limit.
Notation
Set elements are comma-separated text labels. Logic operators and relation-pair notation are documented in the relevant input labels.
Calculator-specific rule
Uses modern Boolean logic without existential import for universal statements.
