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Axiomatizing first order consequences in inclusion logic
Author(s) -
Yang Fan
Publication year - 2020
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201900031
Subject(s) - mathematics , second order logic , expressive power , inclusion (mineral) , natural deduction , higher order logic , calculus (dental) , arithmetic , discrete mathematics , computer science , description logic , theoretical computer science , medicine , dentistry , gender studies , sociology
Abstract Inclusion logic is a variant of dependence logic that was shown to have the same expressive power as positive greatest fixed‐point logic. Inclusion logic is not axiomatisable in full, but its first order consequences can be axiomatized. In this paper, we provide such an explicit partial axiomatization by introducing a system of natural deduction for inclusion logic that is sound and complete for first order consequences in inclusion logic.