Formal Proof of Validity Calculator

Calculator

Premises S -> R S

Enter one premise on each line.

Conclusion Proof output Truth table and rule notes Prefer rule notes Prefer truth table

Show truth table

Show counterexamples

Show Plotly graph

Supported symbols

• NOT: ~ or ¬
• AND: & or ∧
• OR: | or ∨
• IF...THEN: -> or →
• IFF: <-> or ↔
• Use parentheses for grouping.

Construction example:

Premise 1: S -> R

Premise 2: S

Conclusion: R

Check Validity

Example Data Table

Formula Used

An argument is valid when no truth-table row makes every premise true and the conclusion false. The calculator also tests the implication form: ((P1 ∧ P2 ∧ ... ∧ Pn) → C). If that statement stays true on every row, the argument is valid.

This works well for structured construction reasoning, compliance checks, specification dependencies, sequencing rules, and review workflows where conclusions must follow from stated conditions.

How to Use This Calculator

1. Enter one premise per line in the premises field.
2. Enter the target conclusion in the conclusion field.
3. Choose whether you want truth-table emphasis, rule notes, or both.
4. Keep the truth table, counterexample, and graph options checked if you want full output.
5. Press Check Validity to place the result above the form.
6. Review the validity status, proof notes, and any counterexample rows.
7. Download the truth data as CSV or save the report as PDF.

Frequently Asked Questions

1. What does validity mean here?

The argument is valid when every row that satisfies all premises also satisfies the conclusion. One counterexample row makes the argument invalid.

2. Can I use construction-specific variable names?

Yes. Use letters or short names like S, R, PERMIT, or CHECK1. Keep symbols consistent across premises and the conclusion.

3. Which operators are supported?

You can use NOT, AND, OR, implication, and biconditional with symbols such as ~, &, |, ->, and <->.

4. Why is a counterexample important?

A counterexample shows the exact variable assignment where the premises hold but the conclusion fails. It proves the argument is not valid.

5. Does this create full natural deduction proofs?

It gives rule-based proof notes for common patterns and always provides the truth-table test. Complex derivations may still need manual presentation.

6. How many variables should I use?

Try to stay at ten or fewer variables. Larger sets create very large truth tables and make review slower.

7. What are common valid patterns?

Common patterns include Modus Ponens, Modus Tollens, Hypothetical Syllogism, Disjunctive Syllogism, Simplification, and Conjunction.

8. Can I export results for review records?

Yes. Use CSV for row data and PDF for a quick report that can support review notes, audit files, and documentation.