Abstract
In this paper we introduce a calculus based on ordered resolution for Coalition Logic (CL), improving our previous approach based on unrefined resolution, and discuss the problems associated with imposing an ordering refinement in the context of CL. The calculus operates on ‘coalition problems’, a normal form for CL where we use coalition vectors that can represent choices made by agents explicitly, and the inference rules of the calculus provide the basis for a decision procedure for the satisfiability problem in CL. We give correctness, termination and complexity results for our calculus. We also present experimental results for an implementation of the calculus and show that it outperforms a tableau-based decision procedure for Alternating-Time Temporal Logic (CL) on two classes of benchmark formulae for CL.
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References
Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. J. ACM 49(5), 672–713 (2002)
Areces, C., Gennari, R., Heguiabehere, J., de Rijke, M.: Tree-Based heuristic in modal theorem proving. In: Proc. ECAI 2000. IOS Press (2000)
Areces, C., Gorín, D.: Resolution with order and selection for hybrid logics. J. of Automated Reasoning 46, 1–42 (2011), doi:10.1007/s10817-010-9167-0
Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 19–99. Elsevier (2001)
Borgo, S.: Coalitions in action logic. In: Proc. IJCAI 2007, pp. 1822–1827 (2007)
David, A.: TATL: Implementation of ATL tableau-based decision procedure. In: Galmiche, D., Larchey-Wendling, D. (eds.) TABLEAUX 2013. LNCS, vol. 8123, pp. 97–103. Springer, Heidelberg (2013)
van Drimmelen, G.: Satisfiability in alternating-time temporal logic. In: Proc. LICS 2003, pp. 208–207. IEEE (2003)
Gainer, P., Hustadt, U., Dixon, C.: CLProver++ (2015), http://cgi.csc.liv.ac.uk/~ullrich/CLProver++/
Goranko, V.: Coalition games and alternating temporal logics. In: Proc. TARK 2001, pp. 259–272. Morgan Kaufmann (2001)
Goranko, V., van Drimmelen, G.: Complete axiomatization and decidability of alternating-time temporal logic. Theor. Comput. Sci. 353(1), 93–117 (2006)
Goranko, V., Shkatov, D.: Tableau-based decision procedures for logics of strategic ability in multiagent systems. ACM Trans. Comput. Log. 11(1), 1–51 (2009)
Hansen, H.H.: Tableau games for coalition logic and alternating-time temporal logic – theory and implementation. Master’s thesis, University of Amsterdam, The Netherlands, October 2004
Horrocks, I., Hustadt, U., Sattler, U., Schmidt, R.A.: Computational modal logic. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic, pp. 181–245. Elsevier (2006)
Hustadt, U., Konev, B.: TRP++: A temporal resolution prover. In: Baaz, M., Makowsky, J., Voronkov, A. (eds.) Collegium Logicum, pp. 65–79. Kurt Gödel Society (2004)
Kovács, L., Voronkov, A.: First-order theorem proving and vampire. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 1–35. Springer, Heidelberg (2013)
Nalon, C., Zhang, L., Dixon, C., Hustadt, U.: A resolution-based calculus for coalition logic. J. Logic Comput. 24(4), 883–917 (2014)
Nalon, C., Zhang, L., Dixon, C., Hustadt, U.: A resolution prover for coalition logic. In: Proc. SR2014. Electron. Proc. Theor. Comput. Sci., vol. 146, pp. 65–73 (2014)
Pauly, M.: Logic for Social Software. Ph.D. thesis, University of Amsterdam, The Netherlands (2001)
Plaisted, D.A., Greenbaum, S.: A structure-preserving clause form translation. J. Symb. Comput. 2, 293–304 (1986)
Schulz, S.: Simple and efficient clause subsumption with feature vector indexing. In: Bonacina, M.P., Stickel, M.E. (eds.) Automated Reasoning and Mathematics. LNCS, vol. 7788, pp. 45–67. Springer, Heidelberg (2013)
Schulz, S.: System description: E 1.8. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR-19 2013. LNCS, vol. 8312, pp. 735–743. Springer, Heidelberg (2013)
Walther, D., van der Hoek, W., Wooldridge, M.: Alternating-time temporal logic with explicit strategies. In: Proc. TARK 2007, pp. 269–278. ACM (2007)
Walther, D., Lutz, C., Wolter, F., Wooldridge, M.: ATL satisfiability is indeed ExpTime-complete. J. Logic Comput. 16(6), 765–787 (2006)
Weidenbach, C., Dimova, D., Fietzke, A., Kumar, R., Suda, M., Wischnewski, P.: SPASS version 3.5. In: Schmidt, R.A. (ed.) CADE-22. LNCS, vol. 5663, pp. 140–145. Springer, Heidelberg (2009)
Zhang, L., Hustadt, U., Dixon, C.: A resolution calculus for branching-time temporal logic CTL. ACM Trans. Comput. Log. 15(1), 10:1–10:38 (2014)
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Hustadt, U., Gainer, P., Dixon, C., Nalon, C., Zhang, L. (2015). Ordered Resolution for Coalition Logic. In: De Nivelle, H. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2015. Lecture Notes in Computer Science(), vol 9323. Springer, Cham. https://doi.org/10.1007/978-3-319-24312-2_12
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DOI: https://doi.org/10.1007/978-3-319-24312-2_12
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