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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 .
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]
In mathematical logic, a Hintikka set is a set of logical formulas whose elements satisfy the following properties: An atom or its conjugate can appear in the set but not both, If a formula in the set has a main operator that is of "conjuctive-type", then its two operands appear in the set,
Propositional logic only considers logical relations between full propositions. First-order logic also takes the internal parts of propositions into account, like predicates and quantifiers . Extended logics accept the basic intuitions behind classical logic and apply it to other fields, such as metaphysics , ethics , and epistemology .
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
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.
Absorption is a valid argument form and rule of inference of propositional logic. [1] [2] The rule states that if implies , then implies and .The rule makes it possible to introduce conjunctions to proofs.
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.