In the logic context, both the terms operator and connective is used. I wish to know what their differences are. Do we use an operator when we have something that effect only one formula and connective when it some sort of connect two formulae and effect both?
2026-03-26 07:57:29.1774511849
What is the difference between operators and connectives?
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An operator is a more general category than connective.
In propositional logic, the only kinds of operators are connectives, which operate on truth values to produce a truth value for the combined formula.
But in predicate logic, we also have quantifiers ($\forall$ (= "for all"), $\exists$ (= "there exists")), which operate on individuals from a domain to compute a truth value. In modal logic, we have modal operators ($\Box$ (= "necessarily"), $\Diamond$ (= "possibly")), which take into account possible worlds. An so on.