. Avron, On modal systems having arithmetical interpretations, The Journal of Symbolic Logic, vol.16, issue.03, pp.935-942, 1984.
DOI : 10.1007/BF00370323

C. Benedikt and . Koch, XPath leashed, ACM Computing Surveys, vol.41, issue.1, 2009.
DOI : 10.1145/1456650.1456653

W. Benedikt, G. Fan, and . Kuper, Structural properties of XPath fragments, Theoretical Computer Science, vol.336, issue.1, pp.3-31, 2005.
DOI : 10.1016/j.tcs.2004.10.030

M. Benedikt, W. Fan, and F. Geerts, XPath satisfiability in the presence of DTDs, J. ACM, vol.55, issue.28, 2008.

M. Blackburn, Y. De-rijke, and . Venema, Modal Logic, volume 53 of Cambridge Tracts in Theoretical Computer Science, 2001.

A. Boja?czyk, T. Muscholl, L. Schwentick, and . Segoufin, Two-variable logic on data trees and XML reasoning, J. ACM, vol.56, issue.3, p.13, 2009.

L. Brünnler and . Straßburger, Modular Sequent Systems for Modal Logic, LNCS, vol.5607, pp.152-166, 2009.
DOI : 10.1007/978-3-642-02716-1_12

V. Chagrov and M. N. Rybakov, How many variables does one need to prove PSPACEhardness of modal logics? In AiML, pp.71-82, 2002.

K. Chandra, D. C. Kozen, and L. J. Stockmeyer, Alternation, Journal of the ACM, vol.28, issue.1, pp.114-133, 1981.
DOI : 10.1145/322234.322243

. Figueira, Alternating register automata on finite words and trees, Logical Methods in Computer Science, vol.8, issue.1, pp.22-2012
DOI : 10.2168/LMCS-8(1:22)2012

. Figueira, Decidability of Downward XPath, ACM Transactions on Computational Logic, vol.13, issue.4, pp.34-2012
DOI : 10.1145/2362355.2362362

. Figueira, On XPath with transitive axes and data tests, Proceedings of the 32nd symposium on Principles of database systems, PODS '13, pp.249-260, 2013.
DOI : 10.1145/2463664.2463675

L. Figueira and . Segoufin, Bottom-up automata on data trees and vertical XPath, STACS 2011, pp.93-104, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00573596

R. Jurdzi?ski and . Lazi?, Alternating automata on data trees and XPath satisfiability, ACM Transactions on Computational Logic, vol.12, issue.3, p.19, 2011.
DOI : 10.1145/1929954.1929956

. Lunel, Systèmes de preuves pour logiques modales à données, 2015.

. Negri, Proof Analysis in Modal Logic, Journal of Philosophical Logic, vol.12, issue.5-6, pp.507-544, 2005.
DOI : 10.1007/s10992-005-2267-3

. Poggiolesi, The Method of Tree-Hypersequents for??Modal??Propositional??Logic, Towards Mathematical Philosophy, pp.31-51, 2009.
DOI : 10.1007/978-1-4020-9084-4_3
URL : https://hal.archives-ouvertes.fr/halshs-00775815

D. Robie, M. Chamberlin, J. Dyck, and . Snelson, XML Path Language (XPath) 3.0. W3C Recommendation, 2014. URL http

C. Ten and M. Marx, Axiomatizing the logical core of XPath 2.0. Theor, Comput. Sys, vol.44, issue.4, pp.561-589, 2009.

G. Ten-cate, T. Fontaine, and . Litak, Some modal aspects of XPath, Journal of Applied Non-Classical Logics, vol.2141, issue.3, pp.139-171, 2010.
DOI : 10.1007/978-94-017-0454-0_2

B. Ten-cate, T. Litak, and M. Marx, Complete axiomatizations for XPath fragments, Journal of Applied Logic, vol.8, issue.2, pp.153-172, 2010.
DOI : 10.1016/j.jal.2009.09.002

. Wansing, Sequent Calculi for Normal Modal Propositional Logics, Journal of Logic and Computation, vol.4, issue.2, pp.125-142, 1994.
DOI : 10.1093/logcom/4.2.125