Undecidability of the logic of Overlap relation over discrete linear orderings

Electronic Notes in Theoretical Computer Science

Volumn 262, Issue , 2010, Pages 65-81

  Bresolin, Davide ^a   Della Monica, Dario ^b   Goranko, Valentin ^c   Montanari, Angelo ^b   Sciavicco, Guido ^d  

^a UNIVERSITY OF VERONA   (Italy)

^b UNIVERSITY OF UDINE   (Italy)

^c TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^d UNIVERSITY OF MURCIA   (Spain)

Author keywords

Interval temporal logics; Octant tiling problem; Overlap relation; Undecidability

Indexed keywords

HYDRAULIC STRUCTURES; SET THEORY; TEMPORAL LOGIC;

INTERVAL STRUCTURES; INTERVAL TEMPORAL LOGIC; LINEAR ORDERINGS; MODAL LOGIC; MODAL OPERATORS; OCTANT TILING PROBLEM; OVERLAP RELATION; UNDECIDABILITY;

COMPUTER CIRCUITS;

EID: 81455129959     PISSN: 15710661     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.entcs.2010.04.006     Document Type: Conference Paper

References (13)

1. J. F. Allen. Maintaining knowledge about temporal intervals. Communications of the ACM, 26(11):832-843, 1983.
2. E. Börger, E. Grädel, and Y. Gurevich. The Classical Decision Problem. Springer, 1997.
3. D. Bresolin, D. Della Monica, V. Goranko, A. Montanari, and G. Sciavicco. Decidable and Undecidable Fragments of Halpern and Shoham's Interval Temporal Logic: Towards a Complete Classification. In Proc. of the 15th Int. Conf. on Logic for Programming, Artificial Intelligence, and Reasoning, volume 5330 of LNCS, pages 590-604. Springer, 2008.
4. D. Bresolin, D. Della Monica, V. Goranko, A. Montanari, and G. Sciavicco. Undecidability of Interval Temporal Logics with the Overlap Modality. In C. Lutz and J. F. Raskin, editors, Proc. of the 16th International Symposium on Temporal Representation and Reasoning, pages 88-95. IEEE Computer Society Press, 2009.
5. D. Bresolin, V. Goranko, A. Montanari, and P. Sala. Tableau-based decision procedures for the logics of subinterval structures over dense orderings. Journal of Logic and Computation, doi:10.1093/logcom/exn063, 2008.
6. D. Bresolin, V. Goranko, A. Montanari, and G. Sciavicco. Propositional Interval Neighborhood Logics: Expressiveness, Decidability, and Undecidable Extensions. Annals of Pure and Applied Logic, 161(3):289-304, 2009.
7. D. Bresolin, A. Montanari, P. Sala, and G. Sciavicco. Optimal Tableaux for Right Propositional Neighborhood Logic over Linear Orders. In Proc. of the 11th European Conference on Logics in AI, volume 5293 of LNAI, pages 62-75. Springer, 2008.
8. Z. Chaochen, C. A. R. Hoare, and A. P. Ravn. A calculus of durations. Inf. Proc. Letters, 40(5):269-276, 1991.
9. J. Halpern and Y. Shoham. A propositional modal logic of time intervals. Journal of the ACM, 38(4):935-962, 1991.
10. K. Lodaya. Sharpening the undecidability of interval temporal logic. In Proc. of the 6th Asian Computing Science Conference, volume 1961 of LNCS, pages 290-298. Springer, 2000. (Pubitemid 33214024)
11. A. Montanari, G. Puppis, and P. Sala. A decidable spatial logic with cone-shaped cardinal directions. In Proc. of the 18th Annual Conference of the EACSL, volume 5771 of LNCS, pages 394-408. Springer, 2009.
12. B. Moszkowski. Reasoning about digital circuits. Tech. rep. stan-cs-83-970, Dept. of Computer Science, Stanford University, Stanford, CA, 1983.
13. I. Shapirovsky and V. Shehtman. Chronological future modality in Minkowski spacetime. In P. Balbiani, N. Y. Suzuki, F. Wolter, and M. Zakharyaschev, editors, Advances in Modal Logic, volume 4, pages 437-459. King's College Publications, London, 2003.