Abstract
This paper presents a method of deciding extended modal formulas that arise, in particular, when reasoning about transformations of relational structures and graphs. The method proceeds by first unwinding a structure that is an over-approximation of potential models, and then selecting effective models with the aid of a SAT solver.
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Areces, C., Fontaine, P., Merz, S.: Modal satisfiability via SMT solving. In: De Nicola, R., Hennicker, R. (eds.) Software, Services, and Systems. LNCS, vol. 8950, pp. 30–45. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-15545-6_5
Baader, F., Lutz, C.: Description logic. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) The Handbook of Modal Logic, pp. 757–820. Elsevier (2006)
Barrett, C., et al.: CVC4. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 171–177. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_14
Bouton, T., Caminha B. de Oliveira, D., Déharbe, D., Fontaine, P.: veriT: an open, trustable and efficient SMT-solver. In: Schmidt, R.A. (ed.) CADE 2009. LNCS (LNAI), vol. 5663, pp. 151–156. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02959-2_12
Brenas, J.H., Echahed, R., Strecker, M.: A hoare-like calculus using the SROIQ\(^{\sigma }\) logic on transformations of graphs. In: Diaz, J., Lanese, I., Sangiorgi, D. (eds.) TCS 2014. LNCS, vol. 8705, pp. 164–178. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44602-7_14
Giunchiglia, E., Tacchella, A., Giunchiglia, F.: SAT-based decision procedures for classical modal logics. J. Autom. Reason. 28(2), 143–171 (2002). https://doi.org/10.1023/A:1015071400913
Haarslev, V., Sebastiani, R., Vescovi, M.: Automated reasoning in \(\cal{ALCQ}\) via SMT. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS (LNAI), vol. 6803, pp. 283–298. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22438-6_22
Jackson, D.: Software Abstractions. MIT Press, Cambridge (2011)
Reynolds, A., Barbosa, H., Fontaine, P.: Revisiting enumerative instantiation. In: Beyer, D., Huisman, M. (eds.) TACAS 2018. LNCS, vol. 10806, pp. 112–131. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89963-3_7
Sebastiani, R., Vescovi, M.: Automated reasoning in modal and description logics via SAT encoding: the case study of K (m)/ALC-satisfiability. J. Artif. Intell. Res. 35(1), 343 (2009)
Acknowledgements
Most of the work described here has been carried out while the author was at Inria Nancy during a research stay financially supported by Inria and hosted by the VeriDis team. I am grateful to Stephan Merz for inviting me, and to him and to Pascal Fontaine for discussions about and suggestions for improvement of this paper.
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Strecker, M. (2018). Deciding Extended Modal Logics by Combining State Space Generation and SAT Solving. In: Fleuriot, J., Wang, D., Calmet, J. (eds) Artificial Intelligence and Symbolic Computation. AISC 2018. Lecture Notes in Computer Science(), vol 11110. Springer, Cham. https://doi.org/10.1007/978-3-319-99957-9_8
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