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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
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===6.37. Propositional Types===
===6.37. Propositional Types===
In this Section I describe a formal system of ''type expressions'' that are analogous to formulas of propositional logic, and I discuss their use as a calculus of predicates for classifying, analyzing, and drawing typical inferences about <math>n\!</math>-place relations, in particular, for reasoning about the results of operations indicated or performed on relations and about the properties of their transformations and combinations.
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Definition. Given a cartesian product XxY, an ordered pair <x, y> C XxY has the type S.T, written <x, y> : S.T, iff x C S c X and y C T c Y. Notice that an ordered pair can have many types.
Definition. Given a cartesian product XxY, an ordered pair <x, y> C XxY has the type S.T, written <x, y> : S.T, iff x C S c X and y C T c Y. Notice that an ordered pair can have many types.