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Propositional logic (also referred to as Sentential logic) refers to a form of logic in which formulae known as "sentences" can be formed by combining other simpler sentences using logical connectives, and a system of formal proof rules allows certain formulae to be established as theorems.
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 .
propositional logic, Boolean algebra The statement ¬ A {\displaystyle \lnot A} is true if and only if A is false. A slash placed through another operator is the same as ¬ {\displaystyle \neg } placed in front.
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]
A second-order propositional logic is a propositional logic extended with quantification over propositions. A special case are the logics that allow second-order Boolean propositions , where quantifiers may range either just over the Boolean truth values , or over the Boolean-valued truth functions .
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.
A propositional proof system is given as a proof-verification algorithm P(A,x) with two inputs.If P accepts the pair (A,x) we say that x is a P-proof of A.P is required to run in polynomial time, and moreover, it must hold that A has a P-proof if and only if A is a tautology.
Download QR code; Print/export Download as PDF; ... Import-export is a name given to the statement as a theorem or truth-functional tautology of propositional logic