Dependence logic with generalized quantifiers: Axiomatizations

descriptionPublicationkeyboard_double_arrow_right Article , Part of book or chapter of book , Preprint , Conference object 01 Jan 2013Embargo end date: 01 Jan 2013 Finland, Netherlands English Publisher:Elsevier BVJournal:Journal of Computer and System Sciences, volume 88, pages 90-102 (issn: 0022-0000,

Copyright policy )Funded by:AKA | Algorithmic Approaches to..., AKA | Mathematical logic and it..., FCT | D4 +1 projects

Authors: Fredrik Engström; Juha Kontinen; Jouko Väänänen;

doi: 10.1016/j.jcss.2017.03.010 , 10.1007/978-3-642-39992-3_14 , 10.48550/arxiv.1304.0611

arXiv: 1304.0611

handle: 11245/1.406594 , 11245.1/55dc9af4-3fc7-4948-bc46-03194852d79c , 10138/214806

Dependence logic with generalized quantifiers: Axiomatizations

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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.

17 pages

Countries

Finland, Netherlands

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Keywords

FOS: Computer and information sciences, Computer Science - Logic in Computer Science, 330, Logic with extra quantifiers and operators, generalized quantifiers, 03C80, Mathematics - Logic, Other nonclassical logic, dependence logic, 004, Logic in Computer Science (cs.LO), Philosophy, FOS: Mathematics, F.4.1, branching quantifiers, natural deduction, Logic (math.LO), Mathematics

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