Modal Logic
Modal logic is historically the earliest area in the study of intensional logic, originally motivated by formalizing "necessity" and "possibility" (recently, this original motivation belongs to alethic logic, just one of the many branches of modal logic).
Modal logic can be regarded also as the most simple appearance of such studies: it extends extensional logic just with a few sentential functors: these are intensional, and they are interpreted (in the metarules of semantics) as quantifying over possible worlds. Moreover, they are related to one another by similar dualities like quantifiers do (for example by the analogous correspondents of De Morgan's laws). Syntactically, they are not quantifiers, they do not bind variables, they appear in the grammar as sentential functors, they are called modal operators.
As mentioned, precursors of modal logic includes Aristotle. Medieval scholastic discussions accompanied its development, for example about de re versus de dicto modalities: said in recent terms, in the de re modality the modal functor is applied to an open sentence, the variable is bound by a quantifier whose scope includes the whole intensional subterm.
Modern modal logic began with the Clarence Irving Lewis, his work was motivated by establishing the notion of strict implication. Possible worlds approach enabled more exact study of semantical questions. Exact formalization resulted in Kripke semantics (developed by Saul Kripke, Jaakko Hintikka, Stig Kanger).
Read more about this topic: Intensional Logic
Famous quotes containing the word logic:
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