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  2. Conjunction elimination - Wikipedia

    en.wikipedia.org/wiki/Conjunction_elimination

    In propositional logic, conjunction elimination (also called and elimination, ∧ elimination, [1] or simplification) [2][3][4] is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true. The rule makes it possible to shorten longer proofs ...

  3. Propositional formula - Wikipedia

    en.wikipedia.org/wiki/Propositional_formula

    Propositional formula. In propositional logic, a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, or a sentential formula.

  4. Propositional calculus - Wikipedia

    en.wikipedia.org/wiki/Propositional_calculus

    Propositional calculus. Not to be confused with Propositional analysis. The propositional calculus[a] is a branch of logic. [1] It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [1] or sometimes zeroth-order logic. [4][5] It deals with propositions [1] (which can be true or false) [6] and ...

  5. Quantifier (logic) - Wikipedia

    en.wikipedia.org/wiki/Quantifier_(logic)

    In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier in the first order formula expresses that everything in the domain satisfies the property denoted by . On the other hand, the existential quantifier in the formula expresses that ...

  6. Prenex normal form - Wikipedia

    en.wikipedia.org/wiki/Prenex_normal_form

    A formula of the predicate calculus is in prenex[1] normal form (PNF) if it is written as a string of quantifiers and bound variables, called the prefix, followed by a quantifier-free part, called the matrix. [2] Together with the normal forms in propositional logic (e.g. disjunctive normal form or conjunctive normal form), it provides a ...

  7. Propositional variable - Wikipedia

    en.wikipedia.org/wiki/Propositional_variable

    In mathematical logic, a propositional variable (also called a sentence letter,[1] sentential variable, or sentential letter) is an input variable (that can either be true or false) of a truth function. Propositional variables are the basic building-blocks of propositional formulas, used in propositional logic and higher-order logics.

  8. Disjunction elimination - Wikipedia

    en.wikipedia.org/wiki/Disjunction_elimination

    Transformation rules. In propositional logic, disjunction elimination[1][2] (sometimes named proof by cases, case analysis, or or elimination) is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof. It is the inference that if a statement implies a statement and a statement ...

  9. DPLL algorithm - Wikipedia

    en.wikipedia.org/wiki/DPLL_algorithm

    O ( n ) {\displaystyle O (n)} (basic algorithm) In logic and computer science, the Davis–Putnam–Logemann–Loveland (DPLL) algorithm is a complete, backtracking -based search algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e. for solving the CNF-SAT problem.