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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.
For example, the connective "and" is truth-functional since a sentence like "Apples are fruits and carrots are vegetables" is true if, and only if, each of its sub-sentences "apples are fruits" and "carrots are vegetables" is true, and it is false otherwise. Some connectives of a natural language, such as English, are not truth-functional.
[2] [34] Sentential connectives are any linguistic particles that bind sentences to create a new compound sentence, [2] [34] or that inflect a single sentence to create a new sentence. [2] A logical connective, or propositional connective, is a kind of sentential connective with the characteristic feature that, when the original sentences it ...
A propositional formula may also be called a propositional expression, a sentence, [1] or a sentential formula. A propositional formula is constructed from simple propositions, such as "five is greater than three" or propositional variables such as p and q, using connectives or logical operators such as NOT, AND, OR, or IMPLIES; for example:
The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...
In this way, the truth value of the compound sentence is defined as a certain truth function of the truth values of the simpler sentences. The connectives are usually taken to be logical constants, meaning that the meaning of the connectives is always the same, independent of what interpretations are given to the other symbols in a formula.
A discourse marker is a word or a phrase that plays a role in managing the flow and structure of discourse.Since their main function is at the level of discourse (sequences of utterances) rather than at the level of utterances or sentences, discourse markers are relatively syntax-independent and usually do not change the truth conditional meaning of the sentence. [1]
Venn diagram of . In logic, mathematics and linguistics, and is the truth-functional operator of conjunction or logical conjunction.The logical connective of this operator is typically represented as [1] or & or (prefix) or or [2] in which is the most modern and widely used.