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On a Decidable Generalized Quantifier Logic Corresponding to a Decidable Fragment of First-Order Logic

Natasha Alechina
Journal of Logic, Language, and Information
Vol. 4, No. 3, Special Issue on Decompositions of First-Order Logic (1995), pp. 177-189
Published by: Springer
Stable URL: http://www.jstor.org/stable/40180070
Page Count: 13
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On a Decidable Generalized Quantifier Logic Corresponding to a Decidable Fragment of First-Order Logic
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Abstract

Van Lambalgen (1990) proposed a translation from a language containing a generalized quantifier Q into a first-order language enriched with a family of predicates Ri, for every arity i (or an infinitary predicate R) which takes Qxø(x,y1, . . . ,yn) to ∀x(R(x,y1, . . . ,yn) → ø(x,y1, . . . ,yn)) (y1, . . . ,yn are precisely the free variables of Qxø). The logic of Q (without ordinary quantifiers) corresponds therefore to the fragment of first-order logic which contains only specially restricted quantification. We prove that it is decidable using the method of analytic tableaux. Related results were obtained by Andréka and Németi (1994) using the methods of algebraic logic.

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