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2. Redundant proof - Wikipedia

   en.wikipedia.org/wiki/Redundant_proof

   The second pattern of potentially globally redundant proofs appearing in global redundancy definition is related to the well-known [further explanation needed] notion of regularity [further explanation needed]. Informally, a proof is irregular if there is a path from a node to the root of the proof such that a literal is used more than once as ...

3. Literal (mathematical logic) - Wikipedia

   en.wikipedia.org/wiki/Literal_(mathematical_logic)

   In mathematical logic, a literal is an atomic formula (also known as an atom or prime formula) or its negation. [1] [2] The definition mostly appears in proof theory (of classical logic), e.g. in conjunctive normal form and the method of resolution. Literals can be divided into two types: [2] A positive literal is just an atom (e.g., ).

4. Rule of inference - Wikipedia

   en.wikipedia.org/wiki/Rule_of_inference

   In the rule (schema) above, the metavariables A and B can be instantiated to any element of the universe (or sometimes, by convention, a restricted subset such as propositions) to form an infinite set of inference rules. A proof system is formed from a set of rules chained together to form proofs, also called derivations. Any derivation has ...

5. Tautology (rule of inference) - Wikipedia

   en.wikipedia.org/wiki/Tautology_(rule_of_inference)

   In propositional logic, tautology is either of two commonly used rules of replacement. [1] [2] [3] The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs. They are: The principle of idempotency of disjunction:

6. Mathematical proof - Wikipedia

   en.wikipedia.org/wiki/Mathematical_proof

   The definition of a formal proof is intended to capture the concept of proofs as written in the practice of mathematics. The soundness of this definition amounts to the belief that a published proof can, in principle, be converted into a formal proof.

7. Method of analytic tableaux - Wikipedia

   en.wikipedia.org/wiki/Method_of_analytic_tableaux

   A proof procedure is a method for actually finding a proof (if one exists). In other words, a tableau calculus is a set of rules, while a proof procedure is a policy of application of these rules. Even if a calculus is complete, not every possible choice of application of rules leads to a proof of an unsatisfiable set.