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Some of those properties that a logical connective may have are: Associativity Within an expression containing two or more of the same associative connectives in a row, the order of the operations does not matter as long as the sequence of the operands is not changed.
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. This is how we define logical connectives in propositional logic: ¬Φ is True iff Φ is False. (Φ ∧ Ψ) is True iff Φ is True and Ψ is True.
Propositional logic, as currently studied in universities, is a specification of a standard of logical consequence in which only the meanings of propositional connectives are considered in evaluating the conditions for the truth of a sentence, or whether a sentence logically follows from some other sentence or group of sentences.
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.
Pages in category "Logical connectives" The following 21 pages are in this category, out of 21 total. This list may not reflect recent changes. ...
Distributivity is a property of some logical connectives of truth-functional propositional logic. The following logical equivalences demonstrate that distributivity is a property of particular connectives. The following are truth-functional tautologies.
This method locates as "1" the principal connective — the connective under which the overall evaluation of the formula occurs for the outer-most parentheses (which are often omitted). [19] It also locates the inner-most connective where one would begin evaluatation of the formula without the use of a truth table, e.g. at "level 6".
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 ...