Propositional Logic Consistency Calculator

Calculator

Enter one premise per line. Supported operators: !, NOT, &, AND, |, OR, ^, XOR, ->, =>, <->, <=>. Use parentheses when needed. Maximum unique variables per run: 8.

Premises p -> q q -> r p

Optional Conclusion

Accepted examples

• p -> q
• (p AND q) -> r
• NOT p OR q
• p <-> q

Run Analysis

The result appears above this form after submission.

Calculate Consistency

Example Data Table

Formula Used

The core consistency test is based on satisfiability. Let the premises be P1, P2, ..., Pn. The set is consistent when there exists at least one valuation v such that:

v(P1 ∧ P2 ∧ ... ∧ Pn) = T

If no valuation makes the conjunction true, the premise set is inconsistent. When a conclusion C is supplied, entailment is checked with:

For every v, if v(P1 ∧ P2 ∧ ... ∧ Pn) = T, then v(C) = T

The calculator evaluates every valuation in the truth table, counts satisfying rows, computes the consistency ratio as satisfying rows / total rows × 100, and identifies counterexamples where the premises are true but the conclusion is false.

How to Use This Calculator

1. Enter one proposition per line in the premises field.
2. Use consistent variable names such as p, q, r, or descriptive labels.
3. Write operators with symbols or words, including AND, OR, NOT, ->, and <->.
4. Add an optional conclusion when you also want an entailment test.
5. Press the calculation button and read the result section shown above the form.
6. Review the truth table, sample models, summary counts, and graph.
7. Download the truth table as CSV or PDF when needed.
8. Use the example table below the form as a reference for expected output style.

FAQs

1. What does consistency mean in propositional logic?

Consistency means at least one truth assignment makes every premise true together. If no assignment satisfies them simultaneously, the set is inconsistent.

2. What does entailment mean here?

Entailment means every truth assignment satisfying the premises also satisfies the conclusion. A single counterexample row is enough to show non-entailment.

3. Why can inconsistent premises still entail a conclusion?

With no satisfying model for the premises, there is no counterexample where premises are true and conclusion is false. That makes entailment vacuously true.

4. Which operators can I use?

You can use NOT, AND, OR, XOR, implication, biconditional, parentheses, and their symbol forms. The parser accepts several common alternatives.

5. Why is there a variable limit?

Truth tables grow exponentially. Eight variables already produce 256 assignments, so limiting variables keeps the page fast and practical.

6. What does the consistency ratio show?

The consistency ratio shows the percentage of all possible truth assignments that satisfy every premise. Larger percentages indicate broader compatibility across models.

7. Can I use descriptive variable names?

Yes. Names such as Rain, Alarm, or ValidInput work, as long as you use them consistently across all propositions.

8. What do the CSV and PDF exports include?

The exports include the visible truth table columns and rows. This makes it easier to document results, share findings, and audit logical evaluations.