Enter proof data
Example data table
| Case | Premises | Conclusion | Key Rule Flow | Expected Outcome |
|---|---|---|---|---|
| Transitive implication | A → B; B → C; A | C | MP, MP | Valid entailment and valid proof. |
| Disjunctive reduction | P ∨ Q; ¬P | Q | DS | Valid entailment and concise proof. |
| Failed support | X → Y; Y | X | Unsupported converse | Counterexample should appear. |
Formula used
Logical entailment test: ((P1 ∧ P2 ∧ ... ∧ Pn) → C)
Consistency test: SAT(P1 ∧ P2 ∧ ... ∧ Pn)
Step accuracy: (Valid proof lines ÷ Total proof lines) × 100
Premise coverage: (Used premises ÷ Entered premises) × 100
Overall score: 30% entailment + 25% step accuracy + 15% conclusion match + 10% premise coverage + 10% well-formedness + 10% consistency
The checker parses each formula into propositional logic syntax, evaluates every truth assignment for the detected variables, and verifies referenced proof rules line by line. This means the result combines semantic validity, structural correctness, and conclusion alignment instead of relying on one score alone.
How to use this calculator
- Enter each premise on its own line.
- Type the target conclusion exactly as intended.
- Write proof steps with the format: statement | rule | references.
- Use valid line numbers in the references field.
- Submit the form to evaluate entailment, consistency, and rule accuracy.
- Review the score cards, proof table, counterexamples, and Plotly chart.
- Download the report as CSV or PDF after checking results.
Frequently asked questions
1. What kind of logic does this checker support?
It supports propositional logic with negation, conjunction, disjunction, implication, and biconditional notation. The proof validator checks several common inference rules used in introductory and intermediate formal reasoning.
2. Does a valid truth-table result guarantee every proof line is correct?
No. Semantic validity only shows the premises entail the conclusion. A proof can still contain a misapplied rule, missing reference, or incorrect intermediate statement.
3. Why can my premises be valid but my proof score stay low?
That usually means the conclusion follows logically, but one or more written steps are malformed, unsupported, or use the wrong justification. The audit table explains which lines need revision.
4. What does consistency mean here?
Consistency means at least one truth assignment makes all premises true together. If the premise set is inconsistent, any conclusion becomes trivially entailed, which weakens real proof quality.
5. What are counterexamples in the report?
A counterexample is a variable assignment where every premise is true but the conclusion is false. Even one counterexample is enough to show the argument is not logically valid.
6. Can I check long formulas with many variables?
Yes, but this page limits analysis to ten distinct variables to keep the truth-table search responsive. Very large proofs are better split into smaller lemmas for review.
7. Which rule names can I type?
You can use aliases such as premise, MP, MT, copy, AndI, AndE, OrI, DN, DS, and HS. Common shorthand like reit or simplification is also recognized.
8. What should I do when a line is marked Check?
Compare the flagged statement with its cited references, confirm the rule actually matches the pattern, and ensure the formula is typed with valid symbols and parentheses.