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SOME OBSERVATIONS ABOUT GENERALIZED QUANTIFIERS IN LOGICS OF IMPERFECT INFORMATION

Published online by Cambridge University Press:  12 April 2019

FAUSTO BARBERO
FAUSTO BARBERO*
Affiliation:
Department of Philosophy, History, Culture and Art Studies, University of Helsinki
*
*DEPARTMENT OF PHILOSOPHY, HISTORY, CULTURE AND ART STUDIES UNIVERSITY OF HELSINKI, P.O. BOX 24 (UNIONINKATU 40 A) FIN - 00014, FINLAND E-mail: fausto.barbero@helsinki.fi
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Abstract

We analyse the two definitions of generalized quantifiers for logics of dependence and independence that have been proposed by F. Engström, comparing them with a more general, higher order definition of team quantifier. We show that Engström’s definitions (and other quantifiers from the literature) can be identified, by means of appropriate lifts, with special classes of team quantifiers. We point out that the new team quantifiers express a quantitative and a qualitative component, while Engström’s quantifiers only range over the latter. We further argue that Engström’s definitions are just embeddings of the first-order generalized quantifiers into team semantics, and fail to capture an adequate notion of team-theoretical generalized quantifier, save for the special cases in which the quantifiers are applied to flat formulas. We also raise several doubts concerning the meaningfulness of the monotone/nonmonotone distinction in this context. In the appendix we develop some proof theory for Engström’s quantifiers.

Keywords

03B6003C80IF logiclogics of dependence and independencegeneralized quantifiersteam semanticshigher order quantifiers
Type
Research Article
Information
The Review of Symbolic Logic , Volume 12 , Issue 3 , September 2019 , pp. 456 - 486
Copyright
Copyright © Association for Symbolic Logic 2019 

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