Logic Inference Visualizer & Truth Table Generator

Interactive Tool for Understanding Logical Entailment

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Formula Input

Notation Guide:
  • ∧ - Logical AND (conjunction)
  • ∨ - Logical OR (disjunction)
  • → - Logical implication (if-then)
  • ↔ - Logical equivalence (if and only if)
  • ¬ - Logical negation (NOT)
  • Variables: A-Z (single) or A1, P2, Q3 (numbered)
Variable Support: You can use up to 8 variables in any combination. Examples: P, Q, R or A1, B2, C3 or mixed like P1, Q, R2

Understanding Truth Tables

Valid Entailment
  • Conclusion is TRUE in all rows where premises are TRUE
  • No counterexamples exist
  • The inference is logically sound
  • Denoted as: KB ⊨ α (KB entails α)
Invalid Entailment
  • At least one row where premises are TRUE but conclusion is FALSE
  • Counterexample exists
  • The inference is not logically valid
  • Denoted as: KB ⊭ α (KB does not entail α)