Abstract
We present two results relating the completeness condition of the 0-approximation for two formalisms: the action description language \({\mathcal A}\) and the situation calculus. The first result suggests that the condition for the situation calculus formalism implies the condition for the action language formalism. The second result indicates that an action theory in \({\mathcal A}\) can sometimes be simplified to an equivalent action theory whose completeness condition is weaker than the original theory for certain queries.
This is a preview of subscription content, log in via an institution to check access.
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
Balduccini, M., Gelfond, M.: Diagnostic Reasoning with A-Prolog. Theory and Practice of Logic Programming 3(4,5), 425–461 (2003)
Baral, C., Gelfond, M.: Reasoning agents in dynamic domains, pp. 257–279. Kluwer Academic Publishers, Dordrecht (2000)
Baral, C., Kreinovich, V., Trejo, R.: Computational complexity of planning and approximate planning in the presence of incompleteness. Artificial Intelligence 122, 241–267 (2000)
Gelfond, M., Lifschitz, V.: Representing actions and change by logic programs. Journal of Logic Programming 17(2,3,4), 301–323 (1993)
Kartha, G.: Soundness and completeness theorems for three formalizations of action. In: Proceedings of the 13th International Joint Conference on Artificial Intelligence, pp. 724–729. Morgan Kaufmann Publishers, San Mateo (1993)
Levesque, H.J.: A completeness result for reasoning with incomplete first-order knowledge bases. In: KR, pp. 14–23 (1998)
Liu, Y., Levesque, H.: Tractable reasoning with incomplete first-order knowledge in dynamic systems with context-dependent actions. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence, IJCAI, Edinburgh, Scotland (2005)
McCarthy, J.: Programs with common sense. In: Proceedings of the Teddington Conference on the Mechanization of Thought Processes, London, pp. 75–91. Her Majesty’s Stationery Office (1959)
McCarthy, J., Hayes, P.: Some philosophical problems from the standpoint of artificial intelligence. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence, vol. 4, pp. 463–502. Edinburgh University Press, Edinburgh (1969)
McDermott, D.: A critique of pure reason. Computational Intelligence 3, 151–160 (1987)
Moore, R.: A formal theory of knowledge and action. In: Hobbs, J., Moore, R. (eds.) Formal theories of the commonsense world. Ablex, Norwood (1985)
Reiter, R.: The frame problem in the situation calculus: A simple solution (sometimes) and a completeness result for goal regression. In: Artificial Intelligence and Mathematical Theory of Computation, pp. 359–380. Academic Press, London (1991)
Son, T.C., Baral, C.: Formalizing sensing actions - a transition function based approach. Artificial Intelligence 125(1-2), 19–91 (2001)
Son, T.C., Tu, P.H.: On the Completeness of Approximation Based Reasoning and Planning in Action Theories with Incomplete Information. In: Int. Conf. on Principles of Knowledge Representation and Reasoning, pp. 481–491 (2006)
Tu, P.H.: Reasoning and Planning With Incomplete Information in the Presence of Static Causal Laws. Ph.D thesis, New Mexico State University (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tran, C.S., Pontelli, E. (2008). Some Results on the Completeness of Approximation Based Reasoning. In: Ho, TB., Zhou, ZH. (eds) PRICAI 2008: Trends in Artificial Intelligence. PRICAI 2008. Lecture Notes in Computer Science(), vol 5351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89197-0_34
Download citation
DOI: https://doi.org/10.1007/978-3-540-89197-0_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89196-3
Online ISBN: 978-3-540-89197-0
eBook Packages: Computer ScienceComputer Science (R0)