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In focused calculi, it is possible to define positive connectives by giving only their introduction rules, with the shape of the elimination rules being forced by this choice. (Symmetrically, negative connectives can be defined in focused calculi by giving only the elimination rules, with the introduction rules forced by this choice.)
Logical connectives can be used to link zero or more statements, so one can speak about n-ary logical connectives. The boolean constants True and False can be thought of as zero-ary operators. Negation is a unary connective, and so on.
In logic, false [1] or untrue is the state of possessing negative truth value and is a nullary logical connective.In a truth-functional system of propositional logic, it is one of two postulated truth values, along with its negation, truth. [2]
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).
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
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In traditional logic, a particular negative categorical proposition, stating that some members of the subject class are not members of the predicate class. [2] [218] or A logical connective (disjunction) that links propositions in a way that the compound proposition is true if at least one of the linked propositions is true. ordered logic
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