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Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or quantifiers. However, all the machinery of propositional logic is included in first-order logic and higher-order logics. In this sense, propositional logic is the foundation of first-order logic and higher-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, 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.
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.
Unlike predicate logic where terms and predicates are the smallest units, propositional logic takes full propositions with truth values as its most basic component. [121] Thus, propositional logics can only represent logical relationships that arise from the way complex propositions are built from simpler ones.
In logic, a clause is a propositional formula formed from a finite collection of literals (atoms or their negations) and logical connectives.A clause is true either whenever at least one of the literals that form it is true (a disjunctive clause, the most common use of the term), or when all of the literals that form it are true (a conjunctive clause, a less common use of the term).
Due to the ability to speak about non-logical individuals along with the original logical connectives, first-order logic includes propositional logic. [7]: 29–30 The truth of a formula such as "x is a philosopher" depends on which object is denoted by x and on the interpretation of the predicate "is a philosopher".
Stoic logic is the system of propositional logic developed by the Stoic philosophers in ancient Greece. It was one of the two great systems of logic in the classical world. It was largely built and shaped by Chrysippus , the third head of the Stoic school in the 3rd-century BCE.