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Can I express variable occurence ranges in logic?I wonder whether there is some way out to express variable occurence range in logic. I have the following query: exists X,Y(p(X) & q(X,Y) & r(Y)) I can use quantifiers and miniscope to express that a variable first occurs, when I view the conjunction right associative (xfy): exists X(p(X) & exists Y(q(X,Y) & r(Y))). In the above I see that a usage of Y starts after the p(X). Similarly I can use quantifiers and miniscope to express that a variable last occurs, when I view the conjunction as left associative (yfx): exists Y(exists X(p(X) & q(X,Y)) & r(Y)). Now in the above I see that the variable X is last used in q(X,Y) and then not anymore. But what I would like to have is a formalism that allows to express both information, start and end of a variable use. Graphically it would express: p(X) & q(X,Y) & r(Y) +X+ +Y+ Is this possible in logic? A logic that would come with semantics, substitution rules, etc.. Somehow I have the feeling it would violate the Frege principle. On the other hand approaches such as Continuation Passing Style formulation could eventually solve the problem. Best Regards By j4n bur53 at 20111010 08:11  LtU Forum  previous forum topic  next forum topic  other blogs  4669 reads

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