Modal operator: Difference between revisions

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{{Unreferenced|date=May 2019|bot=noref (GreenC bot)}}

A '''modal connective''' (or '''modal operator''') is a [[logical connective]] for [[modal logic]]. It is an [[binary function|operator]] which forms [[proposition]]s from propositions. In general, a modal operator has the "formal" property of being non-[[truth function|truth-functional]] in the following sense: The truth-value of composite formulae sometimes depend on factors other than the actual truth-value of their components. In the case of alethic modal logic, a modal operator can be said to be truth-functional in another sense, namely, that of being sensitive only to the distribution of truth-values across possible worlds, actual or not. Finally, a modal operator is "intuitively" characterized by expressing a modal attitude (such as [[Logical truth|necessity]], [[Logical possibility|possibility]], [[belief]], or [[knowledge]]) about the proposition to which the operator is applied. See also Garson, James, "Modal Logic", The Stanford Encyclopedia of Philosophy (Summer 2021 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/sum2021/entries/logic-modal/>

== Syntax for modal operators ==