Negation and partial axiomatizations of dependence and independence logic revisited

Annals of Pure and Applied Logic 170 (9):1128-1149 (2019)
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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.

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Citations of this work

Axiomatizing first order consequences in inclusion logic.Fan Yang - 2020 - Mathematical Logic Quarterly 66 (2):195-216.
Axiomatizations of team logics.Martin Lück - 2018 - Annals of Pure and Applied Logic 169 (9):928-969.
Complete Logics for Elementary Team Properties.Juha Kontinen & Fan Yang - forthcoming - Journal of Symbolic Logic:1-41.
Coherence in inquisitive first-order logic.Ivano Ciardelli & Gianluca Grilletti - 2022 - Annals of Pure and Applied Logic 173 (9):103155.

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References found in this work

Compositional semantics for a language of imperfect information.W. Hodges - 1997 - Logic Journal of the IGPL 5 (4):539-563.
Dependence and Independence.Erich Grädel & Jouko Väänänen - 2013 - Studia Logica 101 (2):399-410.
On definability in dependence logic.Juha Kontinen & Jouko Väänänen - 2009 - Journal of Logic, Language and Information 18 (3):317-332.
From if to bi.Samson Abramsky & Jouko Väänänen - 2009 - Synthese 167 (2):207 - 230.

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