Abstract
In this paper we continue the study of ‘sabotage modal logic’ SML which was suggested by van Benthem. In this logic one describes the progression along edges of a transition graph in alternation with moves of a saboteur who can delete edges. A drawback of the known results on SML is the asymmetry of the two modalities of ‘moving’ and ‘deleting’: Movements are local, whereas there is a global choice for edge deletion. To balance the situation and to obtain a more realistic model for traffic and network problems, we require that also the sabotage moves (edge deletions) are subject to a locality condition. We show that the new logic, called path sabotage logic PSL, already has the same complexities as SML (model checking, satisfiability) and that it lacks the finite model property. The main effort is finding a pruned form of SML-models that can be enforced within PSL and giving appropriate reductions from SML to PSL.
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References
Benthem, J.v.: An essay on sabotage and obstruction. In: Hutter, D., Werner, S. (eds.) Festschrift in Honour of Prof. Jörg Siekmann, Springer, Heidelberg (2002)
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (1995)
Löding, C.h., Rohde, P.h.: Solving the sabotage game is PSPACE-hard. In Proceedings of MFCS 2003. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 531–540. Springer, Heidelberg (2003)
Löding, C.h., Rohde, P.h.: Model checking and satisfiability for sabotage modal logic. In Proceedings of FSTTCS 2003. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 302–313. Springer, Heidelberg (2003)
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Rohde, P. (2004). Moving in a Crumbling Network: The Balanced Case. In: Marcinkowski, J., Tarlecki, A. (eds) Computer Science Logic. CSL 2004. Lecture Notes in Computer Science, vol 3210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30124-0_25
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DOI: https://doi.org/10.1007/978-3-540-30124-0_25
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