Tautology Engine - Free Online Propositional & Symbolic Logic Calculator and Proof Generator

Free online tool for evaluating logical arguments, generating truth tables, and creating logical proofs

Logic Calculator & Proof Generator

Master propositional logic with a powerful, free calculator. Build logical arguments, generate truth tables, and construct step-by-step formal proofs.

Need to learn? Learn from our free Logic Mastery Academy

Enter Your Logic Problem

Add premises and conclusions to evaluate logical arguments

Premises
Enter the propositions that form the basis of your argument
P1
P2
⊢
Conclusions
Enter the conclusions you want to derive from the premises
C1
Symbol Palette

Automatic Symbol Conversion:

  • Type ~ or ! for ¬
  • Type & for ∧
  • Type | for ∨
  • Type -> for →
  • Type <-> for ↔
  • Type T for ⊤
  • Type F for ⊥
What is Propositional Logic?

Propositional logic (also called symbolic logic) is a branch of logic that deals with propositions (statements that are either true or false) and their logical relationships. It forms the foundation of logical reasoning and is essential in mathematics, computer science, and philosophy.

Our free online calculator helps you evaluate complex logical arguments, generate proofs, and analyze truth conditions of propositions using logical operators like AND (∧), OR (∨), NOT (¬), IMPLIES (→), and BICONDITIONAL (↔).

Key Features
  • Free Online Calculator: No registration or payment required
  • Proof Generator: Create step-by-step logical proofs
  • Argument Validation: Check if logical arguments are valid
  • Truth Table Generation: Automatically generate complete truth tables
  • Real-time Validation: Instant syntax checking and error reporting
How to Use the Logic Calculator

1. Enter Premises

Type your premises (assumptions) in the premise fields. Use logical operators like ∧ (and), ∨ (or), → (implies), ↔ (if and only if), and ¬ (not).

2. Enter Conclusions

Enter the conclusions you want to test. The calculator will determine if they logically follow from your premises.

3. Use Symbols

Click on symbols in the symbol palette to insert them, or type shortcuts like "->" for →, "&" for ∧, etc.

4. Evaluate

Click "Evaluate Argument" to see if your argument is valid, view truth tables, and generate proofs.