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  2. Propositional calculus - Wikipedia

    en.wikipedia.org/wiki/Propositional_calculus

    It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [4] [1] or sometimes zeroth-order logic. [ b ] [ 6 ] [ 7 ] [ 8 ] Sometimes, it is called first-order propositional logic [ 9 ] to contrast it with System F , but it should not be confused with first-order logic .

  3. Commutativity of conjunction - Wikipedia

    en.wikipedia.org/wiki/Commutativity_of_conjunction

    In propositional logic, the commutativity of conjunction is a valid argument form and truth-functional tautology. It is considered to be a law of classical logic. It is the principle that the conjuncts of a logical conjunction may switch places with each other, while preserving the truth-value of the resulting proposition. [1]

  4. Material implication (rule of inference) - Wikipedia

    en.wikipedia.org/wiki/Material_implication_(rule...

    In propositional logic, material implication [1] [2] is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- P {\displaystyle P} or Q {\displaystyle Q} and that either form can replace the other in ...

  5. Import–export (logic) - Wikipedia

    en.wikipedia.org/wiki/Import–export_(logic)

    In propositional logic, import-export is a name given to the propositional form of Exportation: (()) (()).This already holds in minimal logic, and thus also in classical logic, where the conditional operator "" is taken as material implication.

  6. List of axiomatic systems in logic - Wikipedia

    en.wikipedia.org/wiki/List_of_axiomatic_systems...

    Classical propositional calculus is the standard propositional logic. Its intended semantics is bivalent and its main property is that it is strongly complete, otherwise said that whenever a formula semantically follows from a set of premises, it also follows from that set syntactically. Many different equivalent complete axiom systems have ...

  7. Propositional formula - Wikipedia

    en.wikipedia.org/wiki/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, [1] or a sentential formula.

  8. Destructive dilemma - Wikipedia

    en.wikipedia.org/wiki/Destructive_dilemma

    Destructive dilemma [1] [2] is the name of a valid rule of inference of propositional logic. It is the inference that, if P implies Q and R implies S and either Q is false or S is false, then either P or R must be false. In sum, if two conditionals are true, but one of their consequents is false, then one of their antecedents has to be false.

  9. Well-formed formula - Wikipedia

    en.wikipedia.org/wiki/Well-formed_formula

    In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language.