Negation and partial axiomatizations of dependence and independence logic revisited

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Yang , F 2019 , ' Negation and partial axiomatizations of dependence and independence logic revisited ' , Annals of Pure and Applied Logic , vol. 170 , no. 9 , pp. 1128-1149 . https://doi.org/10.1016/j.apal.2019.04.010

Title: Negation and partial axiomatizations of dependence and independence logic revisited
Author: Yang, Fan
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2019-09
Language: eng
Number of pages: 22
Belongs to series: Annals of Pure and Applied Logic
ISSN: 0168-0072
URI: http://hdl.handle.net/10138/330869
Abstract: In this paper, we axiomatize the negatable consequences in dependence and independence logic by extending the systems of natural deduction of the logics given in [22) and [11]. We prove a characterization theorem for negatable formulas in independence logic and negatable sentences in dependence logic, and identify an interesting class of formulas that are negatable in independence logic. Dependence and independence atoms, first-order formulas belong to this class. We also demonstrate our extended system of independence logic by giving explicit derivations for Armstrong's Axioms and the Geiger-Paz-Pearl axioms of dependence and independence atoms. (C) 2019 Elsevier B.V. All rights reserved.
Subject: Dependence logic
Team semantics
Negation
Existential second-order logic
TEAM SEMANTICS
INCLUSION
111 Mathematics
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