A. Arnold and D. Niwi´nskiniwi´nski, Rudiments of mu-calculus, 2001.

V. Bárány and M. Boja´nczykboja´nczyk, Finite satisfiability for guarded fixpoint logic, Information Processing Letters, vol.112, issue.10, pp.371-375, 2012.
DOI : 10.1016/j.ipl.2012.02.005

V. Bárány, B. Cate, and L. Segoufin, Guarded negation, ICALP, 2011.

V. Bárány, B. Cate, and M. Otto, Queries with guarded negation, pp.1328-1339, 2012.

J. Barwise and Y. N. Moschovakis, Abstract, The Journal of Symbolic Logic, vol.36, issue.03, pp.521-534, 1978.
DOI : 10.2307/2371731

M. Benedikt, B. Ten-cate, T. Colcombet, M. Vanden, and . Boom, The Complexity of Boundedness for Guarded Logics, 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science, 2015.
DOI : 10.1109/LICS.2015.36

M. Bienvenu, D. Calvanese, M. Ortiz, and M. Simkus, Nested regular path queries in description logics, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01117593

A. Blumensath, T. Colcombet, D. Kuperberg, P. Parys, M. Vanden et al., Two-way cost automata and cost logics over infinite trees, Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), CSL-LICS '14, 2014.
DOI : 10.1145/2603088.2603104

A. Blumensath, M. Otto, and M. Weyer, Decidability Results for the Boundedness Problem, Logical Methods in Computer Science, vol.10, issue.3, p.2014
DOI : 10.2168/LMCS-10(3:2)2014

P. Bourhis, M. Krötzsch, and S. Rudolph, Reasonable highly expressive query languages, IJCAI, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01211282

D. Calvanese, G. De-giacomo, M. Lenzerini, and M. Y. Vardi, Containment of conjunctive regular path queries with inverse, KR, 2000.

T. Colcombet and C. Löding, Regular Cost Functions over Finite Trees, 2010 25th Annual IEEE Symposium on Logic in Computer Science, 2010.
DOI : 10.1109/LICS.2010.36
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.167.4696

S. S. Cosmadakis, H. Gaifman, P. C. Kanellakis, and M. Y. Vardi, Decidable optimization problems for database logic programs, Proceedings of the twentieth annual ACM symposium on Theory of computing , STOC '88, 1988.
DOI : 10.1145/62212.62259

E. A. Emerson and C. S. Jutla, The complexity of tree automata and logics of programs (extended abstract), FOCS, 1988.

E. Grädel and I. Walukiewicz, Guarded fixed point logic, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158), 1999.
DOI : 10.1109/LICS.1999.782585

E. Grädel, M. Otto, and E. Rosen, Undecidability results on twovariable logics, STACS, 1997.

E. Grädel, C. Hirsch, and M. Otto, Back and forth between guarded and modal logics, ACM Transactions on Computational Logic, vol.3, issue.3, pp.418-463, 2002.
DOI : 10.1145/507382.507388

G. G. Hillebrand, P. C. Kanellakis, H. G. Mairson, and M. Y. Vardi, Undecidable boundedness problems for datalog programs, The Journal of Logic Programming, vol.25, issue.2, pp.163-190, 1995.
DOI : 10.1016/0743-1066(95)00051-K
URL : http://doi.org/10.1016/0743-1066(95)00051-k

N. Immerman, Relational queries computable in polynomial time, 24] C. Löding. Automata on infinite trees, pp.86-104, 1986.
DOI : 10.1016/S0019-9958(86)80029-8
URL : http://doi.org/10.1016/s0019-9958(86)80029-8

M. Otto, The Boundedness Problem for Monadic Universal First-Order Logic, 21st Annual IEEE Symposium on Logic in Computer Science (LICS'06), 2006.
DOI : 10.1109/LICS.2006.50
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.594.6567

M. O. Rabin, Decidability of second-order theories and automata on infinite trees, Trans. Amer. Math. Soc, vol.141, pp.1-35, 1969.

S. Rudolph and M. Krötzsch, Flag & check, Proceedings of the 32nd symposium on Principles of database systems, PODS '13, 2013.
DOI : 10.1145/2463664.2465227

D. Scott, A decision method for validity of sentences in two variables, JSL, vol.27, issue.477, 1962.

L. Segoufin and B. Cate, Unary negation, Logical Methods in Computer Science, vol.9, issue.3, p.2013
DOI : 10.2168/LMCS-9(3:25)2013
URL : https://hal.archives-ouvertes.fr/hal-00573634

W. Thomas, Languages, Automata, and Logic, Handbook of Formal Languages, 1997.
DOI : 10.1007/978-3-642-59126-6_7
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.363.8502

M. Y. Vardi, Reasoning about the past with two-way automata, ICALP, 1998.
DOI : 10.1007/BFb0055090
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.397.6288