Example image of eyePlorer eyePlorer map for 'Rule of inference': Formal system Logic Syntax (logic) Deductive system Formal language Axiom Axiom schema Formal proof Validity Conclusion Premise Theorem Effective method Ω-consistent theory Proof Modus ponens Modus tollens Predicate logic Quantification Mathematical logic Well-formed formula Intuitionistic logic Modal logic Temporal logic Quantum logic Infinity Proposition Natural deduction Natural number Mathematical induction Cut-elimination theorem Sequent calculus Turnstile (symbol) Peano axioms Admissible rule Armstrong's axioms Biconditional introduction Formalism (mathematics) Forward chaining Generalization (logic) Law of thought List of rules of inference Logical harmony Modus ponendo tollens Proof calculus Simplification Soundness Structural rule Transposition (logic) Backward chaining