Interpolation for a Sequent Calculus of Generalized Quantifiers
نویسنده
چکیده
Van Lambalgen (1991) proposed a translation from a language containing a generalized quanti er Q into a rst-order language enriched with a family of predicates R i , for every arity i (or an in nitary predicate R) which takes Qx (x; y 1 ; : : : ; y n ) to 8x(R(x; y 1 ; : : : ; y n ) ! (x;y 1 ; : : : ; y n )) (y 1 ; : : : ; y n are precisely the free variables of Qx ). The logic of Q (without ordinary quanti ers) corresponds therefore to the fragment of rst-order logic which contains only specially restricted quanti cation. We prove that this logic (and the corresponding fragment) has the interpolation property.
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