Logic Foundations — 8 tools
Classical argument structure: premises, conclusions, validity, formal notation. This is the shelf for introductory logic work. If you don't yet trust your syllogism intuitions, start at the top.
Syllogism Validator with Ambiguity Detector
Tests a classic three-part syllogism for validity, then double-checks the premises for the two silent killers: equivocation and undistributed middle.
What this checks
- Figure & mood: AAA-1 (Barbara), EAE-1 (Celarent), AII-1 (Darii), etc.
- Equivocation: same key term used with two different senses across premises.
- Undistributed middle: middle term never covers its class.
- Illicit minor/major: term distributed in conclusion but not in premise.
How to interpret the verdict
"Valid" means the conclusion follows assuming the terms mean the same thing. The verdict can still be unsound if a premise is factually wrong. Two syllables' worth of honesty: most "valid" syllogisms in everyday speech turn out to be invalid once you look at the figure.
FAQ
Why does it say "suspicious figure 2"? Moods like EAE-2 are valid forms but rare in everyday English, so a typo often hides in there.
Can it handle quantifiers other than All/Some/None? Only A/E/I/O (universal affirmative, universal negative, particular affirmative, particular negative). Most non-technical people don't draft syllogisms using rarer forms, so we kept the parser strict on purpose.
What's the limitation? Polysyllogisms (chains) and modal logic. Use a chain in your head and break it into pieces.
Truth Table Builder
Type an expression like (A && B) || !C and a full, ordered truth table comes out. Result column is highlighted row-by-row.
Use ! (NOT), && (AND), || (OR), ^ (XOR), -> (implication A→B becomes !A||B), <-> (biconditional). Variables are any single letter.
Why we sequence by 0,8,4,12… instead of binary
Common "first variable flips at every row" tables make the leftmost column boring. By interleaving the count (Gray-ish), we make every column carry roughly equal information — easier to verify visually when the expression involves 4+ variables. It also matches what most textbook truth-tables show in column order.
If you want pure binary, click "Build table" twice; the second pass orders rows by integer reading of the variable tuple.
Tautology / Contradiction Checker with Proof Tree
Tells you whether a formula is a tautology, contradiction or contingent — then draws a short natural-deduction sketch.
What "tautology" actually means here
A formula is tautological iff it is true in every row of its truth table. A contradiction iff false in every row. Contingent otherwise. Our checker is row-by-row, not analytic — meaning it gives the right answer even for ugly formulas, but doesn't tell you why.
The "proof sketch" we draw is heuristic. It looks for patterns like (A→B) + A and suggests the matching Modus Ponens step. Do not treat it as a certified theorem-prover output.
FAQ
Why no "valid" / "unsatisfiable" labels? In propositional logic, tautology <=> valid, contradiction <=> unsatisfiable. We picked the friendlier words on purpose.
How many variables is too many? We refuse 9+ because the table becomes unreadable. For larger problems, look up a SAT solver — this isn't one.
Will you add quantifier support? Probably not as the same tool. Use the Predicate translator (#4) for first-order work.
Predicate Logic ↔ English Translator
Type a sentence in predicate logic (∀ ∃ ¬ ∧ ∨ → ↔) and get a plain-English paraphrase — and vice versa.
Notes on faithful translation
Multiple English sentences translate to the same formula. "Every student knows a language", "If x is a student, x knows a language" and "All students know some language" all map to ∀x (Student(x) → ∃y (Language(y) ∧ Knows(x,y))). The tool picks one canonical reading; you can edit and re-translate.
Formal Fallacy Classifier & Quiz
Quick reference of 18 named fallacies plus a random multiple-choice quiz mode with rationale after each answer.
What's the most over-applied fallacy?
Straw man is the easy one to spot in others and the hardest in your own writing. The quiz weights it for that reason — over half of "fake" internet arguments are straw men distorted by quote-trimming. The Classifier also catches affirming the consequent far more often than its textbook reputation suggests, because the form P→Q, Q, ∴P shows up in everyday reasoning a lot.
What the classifier will not catch: informal fallacies that depend on tone or context (e.g. "tone policing", "motte-and-bailey" outside the literal bailey). For those, read the prose yourself.
Logic-Gate Circuit Simulator
Compose AND / OR / NOT / XOR gates from a sidebar into a circuit. Output truth table updates live.
The simulator evaluates left-to-right using postfix. For half-adder you can drop (A AND B) followed by NOT (A AND B) — the latter is the "carry" of A∧B.
Why no wire / canvas drag-drop?
A drag-and-drop logic-circuit editor is great for kids but adds a lot of layout code that does not earn its keep for a teaching tool about logic patterns. By keeping the circuit as an ordered list (think RPN), the user focuses on the formula (A && B) as data, which translates to Karnaugh maps, NAND-only synthesis and other textbook exercises downstream.
If you find this too primitive and want a real circuit editor, point me at one and I'll link it.
Karnaugh Map Visualiser
Click cells where the function is true. We auto-group the cells into the smallest sum-of-products and show the simplified expression.
Click toggles a cell. The grouping algorithm is greedy: largest group first, then subtract used minterms, then look for prime implicants.
Simplified expression
Prime implicants
Limits of the greedy grouper
K-map grouping is, for some inputs, NP-hard to do optimally. Our greedy solver is fast and usually right but can pick 3 groups of size 4 where a 4+4+2 choice is possible. The good news: greedy is correct for 2 and 3 variables, optimal for most 4-variable cases you see in class, and "good enough" for the rest.
Argument Map Constructor
Paste an argument. We split sentences, classify them as claim or premise (heuristic) and render a simple map.
Rendering uses straight HTML/SVG; for graphs > 12 nodes the layout switches to a column drop. Pan with mouse.