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Dependence logic with generalized quantifiers: Axiomatizations

Journal article
Authors Fredrik Engström
Juha Kontinen
Jouko Väänänen
Published in Journal of computer and system sciences
Volume 88
Pages 90-102
ISSN 0022-0000
Publication year 2017
Published at Department of Philosophy, Linguistics and Theory of Science
Pages 90-102
Language en
Links dx.doi.org/10.1016/j.jcss.2017.03.0...
Keywords Dependence logic; Generalized quantifiers; Branching quantifiers; Natural deduction
Subject categories Mathematical logic, Logic

Abstract

We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result considers the extension of dependence logic where Q is interpreted as “there exists uncountable many.” Both of the axiomatizations are shown to be sound and complete for FO(Q) consequences.

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