We investigate the properties of Inclusion Logic, that is, First Order Logic with Team Semantics extended with inclusion dependencies. We prove that Inclusion Logic is equivalent to Greatest Fixed Point Logic, and we prove that all union-closed first-order definable properties of relations are definable in it. We also provide an Ehrenfeucht-Fraïssé game for Inclusion Logic, and give an example illustrating its use.
@InProceedings{galliani_et_al:LIPIcs.CSL.2013.281, author = {Galliani, Pietro and Hella, Lauri}, title = {{Inclusion Logic and Fixed Point Logic}}, booktitle = {Computer Science Logic 2013 (CSL 2013)}, pages = {281--295}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-60-6}, ISSN = {1868-8969}, year = {2013}, volume = {23}, editor = {Ronchi Della Rocca, Simona}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2013.281}, URN = {urn:nbn:de:0030-drops-42031}, doi = {10.4230/LIPIcs.CSL.2013.281}, annote = {Keywords: Dependence Logic, Team Semantics, Fixpoint Logic, Inclusion} }
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