Abstract
Van Lambalgen (1990) proposed a translation from a language containing a generalized quantifierQ into a first-order language enriched with a family of predicatesR i, for every arityi (or an infinitary predicateR) which takesQxg(x, y1,..., yn) to ∀x(R(x, y1,..., y1) →Φ(x,y1,...,yn)) (y 1,...,yn are precisely the free variables ofQxΦ). The logic ofQ (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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References
Alechina, N. and van Lambalgen, M., 1995a, “Correspondence and completeness for generalized quantifiers”,Bulletin of IGPL 3, 167–190.
Alechina, N. and van Lambalgen, M., 1995b, “Generalized quantification as substructural logic”, ILLC Report ML-95-05, University of Amsterdam. To appear inJournal of Symbolic Logic.
Andréka, H. and Németi, J. 1994, “Decidability of the bounded fragment of first order logic with equality”, manuscript.
Andréka, H., van Benthem, J., and Németi, L, 1995, “Back and forth between modal logic and classical logic”,Bulletin of IGPL 3, 685–720.
Blackburn, P. and Seligman, J., 1995, “Hybrid Languages”, this issue ofJournal of Logic, Language and Information.
Fine, K., 1985, “Natural deduction and arbitrary objects”,Journal of Philosophical Logic 14, 57–107.
Németi, I., 1992 “Decidability of weakened versions of first order logic and cylindric relativized set algebras”, to appear inLogic Colloquium' 92, L. Csirmaz, D.M. Gabbay, and M. de Rijke, eds., Stanford: CSLI.
Simon, A. and van Lambalgen, M., 1994, “Axiomatizing cylindric relativized set algebras with generalized quantification”, manuscript.
Smullyan, R.M., 1968,First-Order Logic, Berlin: Springer-Verlag.
Van Benthem, J., 1994 “Modal foundations for predicate logic”,Studia Logica, to appear.
Van Benthem, J. and Alechina, N., 1993 “Modal quantification over structured domains”, ILLC Report ML-93-02, University of Amsterdam. To appear inAdvances in Intensional Logic, M. de Rijke, ed., Dordrecht: Kluwer.
van Lambalgen, M., 1990, “The axiomatization of randomness”,Journal of Symbolic Logic 55, 1143–1167.
Van Lambalgen, M., 1991, “Natural deduction for generalized quantifiers”, inGeneralized Quantifier Theory and Applications, J. van der Does and J. van Eijck, eds., Amsterdam: Dutch Network for Language, Logic and Information. To appear as CSLI Lecture Notes.
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Alechina, N. On a decidable generalized quantifier logic corresponding to a decidable fragment of first-order logic. J Logic Lang Inf 4, 177–189 (1995). https://doi.org/10.1007/BF01049411
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DOI: https://doi.org/10.1007/BF01049411