Abstract
We extend the language of here-and-there logic by two kinds of atomic programs allowing to minimally update the truth value of a propositional variable here or there, if possible. These atomic programs are combined by the usual dynamic logic program connectives. We investigate the mathematical properties of the resulting extension of equilibrium logic: we prove that the problem of logical consequence in equilibrium models is EXPTIME complete by relating equilibrium logic to dynamic logic of propositional assignments.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
AlchourrĆ³n, C., GƤrdenfors, P., Makinson, D.: On the logic of theory change: Partial meet contraction and revision functions. J. of Symbolic LogicĀ 50, 510ā530 (1985)
Balbiani, P., Herzig, A., Troquard, N.: Dynamic logic of propositional assignments: a well-behaved variant of PDL. In: Kupferman, O. (ed.) Logic in Computer Science (LICS), New Orleans, June 25-28. IEEE (2013), http://www.ieee.org/
Eiter, T., Fink, M., Sabbatini, G., Tompits, H.: Using methods of declarative logic programming for intelligent information agents. TPLPĀ 2(6), 645ā709 (2002)
FariƱas del Cerro, L., Herzig, A.: Contingency-based equilibrium logic. In: Delgrande, J.P., Faber, W. (eds.) LPNMR 2011. LNCS, vol.Ā 6645, pp. 223ā228. Springer, Heidelberg (2011), http://www.springerlink.com
FariƱas del Cerro, L., Herzig, A.: The modal logic of equilibrium models. In: Tinelli, C., Sofronie-Stokkermans, V. (eds.) FroCoS 2011. LNCS, vol.Ā 6989, pp. 135ā146. Springer, Heidelberg (2011), http://www.springerlink.com
Fischer-Servi, G.: On modal logic with an intuitionistic base. Studia LogicaĀ 36(4), 141ā149 (1976)
Gebser, M., Kaufmann, B., Neumann, A., Schaub, T.: Conflict-driven answer set solving. In: Veloso, M.M. (ed.) IJCAI, pp. 386ā392 (2007)
Gebser, M., Ostrowski, M., Schaub, T.: Constraint answer set solving. In: Hill, P.M., Warren, D.S. (eds.) ICLP 2009. LNCS, vol.Ā 5649, pp. 235ā249. Springer, Heidelberg (2009)
Herzig, A., Lorini, E., Moisan, F., Troquard, N.: A dynamic logic of normative systems. In: Walsh, T. (ed.) International Joint Conference on Artificial Intelligence (IJCAI), Barcelona, pp. 228ā233. IJCAI/AAAI (2011), Erratum at http://www.irit.fr/~Andreas.Herzig/P/Ijcai11.html
van der Hoek, W., Walther, D., Wooldridge, M.: On the logic of cooperation and the transfer of control. J. of AI Research (JAIR)Ā 37, 437ā477 (2010)
van der Hoek, W., Wooldridge, M.: On the dynamics of delegation, cooperation and control: a logical account. In: Proc. AAMAS 2005 (2005)
van der Hoek, W., Wooldridge, M.: On the logic of cooperation and propositional control. Artif. Intell.Ā 164(1-2), 81ā119 (2005)
Katsuno, H., Mendelzon, A.O.: On the difference between updating a knowledge base and revising it. In: GƤrdenfors, P. (ed.) Belief Revision, pp. 183ā203. Cambridge University Press (1992); preliminary version in Allen, J.A., Fikes, R., and Sandewall, E. (eds.) Principles of Knowledge Representation and Reasoning: Proc. 2nd Int. Conf., pp. 387ā394. Morgan Kaufmann Publishers (1991)
Lifschitz, V., Pearce, D., Valverde, A.: Strongly equivalent logic programs. ACM Transactions on Computational LogicĀ 2(4), 526ā541 (2001)
Slota, M., Leite, J.: Robust equivalence models for semantic updates of answer-set programs. In: Brewka, G., Eiter, T., McIlraith, S.A. (eds.) KR. AAAI Press (2012)
Slota, M., Leite, J.: A unifying perspective on knowledge updates. In: del Cerro, L.F., Herzig, A., Mengin, J. (eds.) JELIA 2012. LNCS, vol.Ā 7519, pp. 372ā384. Springer, Heidelberg (2012)
Zhang, Y., Foo, N.Y.: A unified framework for representing logic program updates. In: Veloso, M.M., Kambhampati, S. (eds.) AAAI, pp. 707ā713. AAAI Press/The MIT Press (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
Ā© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
del Cerro, L.F., Herzig, A., Su, E.I. (2013). Combining Equilibrium Logic and Dynamic Logic. In: Cabalar, P., Son, T.C. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2013. Lecture Notes in Computer Science(), vol 8148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40564-8_30
Download citation
DOI: https://doi.org/10.1007/978-3-642-40564-8_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40563-1
Online ISBN: 978-3-642-40564-8
eBook Packages: Computer ScienceComputer Science (R0)