Fallacy Files archives writing about logical fallacies and related weblog posts.
Umsu
Umsu offers a reference for mathematical and logical symbols, including connectives and quantifiers.
About Umsu
The Tree Proof Generator accepts a formula in standard propositional, predicate, or modal logic and tries to find either a countermodel or a tree proof, also called a semantic tableau. Arguments with premises can be tested by separating premises with commas and using |= before the conclusion. It supports classical propositional logic and first-order predicate logic with functions and identity, plus selected normal modal logics with a choice of accessibility constraints. For modal predicate logic it assumes constant domains and rigid terms, and input must follow defined rules for symbols, precedence, and prefix notation.
Key features
- Finds countermodel or tree proof for entered formula
- Checks arguments with premises separated by |= notation
- Supports classical propositional and first-order predicate logic
- Supports selected normal modal logics with accessibility choices
- Enters symbols via buttons, keyboard shortcuts, or LaTeX
- Parses functions, identity, and prefix-notation predicates
Best for: Students and instructors working with propositional, predicate, or modal logic.
Good for
- Covers propositional, predicate, and modal logic in one page
- Returns either a tree proof or a countermodel
- Accepts typed shortcuts and LaTeX commands for symbols
Watch out for
- Requires strict syntax including prefix notation and full quantifier sequences
- Assumes constant domains and rigid terms for modal predicate logic
- Supports only a few normal modal logics
Umsu at a glance
- Website
- umsu.de/trees
- Category
- Education & Learning › History & Humanities
- Type
- Website
- Pricing
- Not confirmed. Check the site
- Platforms
- Web
- Open source
- Not stated
- Language
- English
- Last checked
- Oct 5, 2026 · Online when checked
- Listed
- Oct 5, 2026
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Umsu FAQ
How do I enter logic symbols?
Use the buttons above the text field, or type ~ for ¬, & for ∧, v for ∨, -> for →, for ↔, ! for ∀, ? for ∃, [] for □. LaTeX commands can also be used.
How do I test an argument with premises?
Separate premises with commas and use |= between the premises and the conclusion, for example p∨q, ¬p |= q.
Which logics are supported?
Classical propositional logic and first-order predicate logic with functions and identity, plus a few normal modal logics. Modal predicate logic assumes constant domains and rigid terms.
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