Abstract
Nonmonotonic causal logic can be used to represent properties of actions, including actions with conditional and indirect effects, nondeterministic actions, and concurrently executed actions. The definite fragment of causal logic can be mapped to propositional logic by the process of completion, and this idea has led to the development of the Causal Calculator. In this note, we show how to turn arbitrary causal theories into definite theories without changing the sets of models. The translation consists of two parts: one is a set of definite rules which is obtained from the given theory by translating each rule one by one, in a modular way, and the other is a set of constraints similar to loop formulas for logic programs. Our result characterizes the semantics of causal logic in terms of propositional logic and tells us that an essential difference between the semantics of causal logic and the answer set semantics is related to the definition of a loop in each.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Akman, V., Erdoğan, S., Lee, J., Lifschitz, V., Turner, H.: Representing the Zoo World and the Traffic World in the language of the Causal Calculator. Artificial Intelligence (2003) (to appear), http://www.cs.utexas.edu/users/appsmurf/papers/zt.ps
Artikis, A., Sergot, M., Pitt, J.: An executable specification of an argumentation protocol. In: Proceedings of Conference on Artificial Intelligence and Law (ICAIL), pp. 1–11. ACM Press, New York (2003)
Artikis, A., Sergot, M., Pitt, J.: Specifying electronic societies with the Causal Calculator. In: Giunchiglia, F., Odell, J.J., Weiss, G. (eds.) AOSE 2002. LNCS, vol. 2585, pp. 1–15. Springer, Heidelberg (2003)
Campbell, J., Lifschitz, V.: Reinforcing a claim in commonsense reasoning. In: Working Notes of the AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning (2003), http://www.cs.utexas.edu/users/vl/papers/sams.ps
Chopra, A., Singh, M.: Nonmonotonic commitment machines. In: Agent Communication Languages and Conversation Policies AAMAS 2003 Workshop (2003)
Clark, K.: Negation as failure. In: Gallaire, H., Minker, J. (eds.) Logic and Data Bases, pp. 293–322. Plenum Press, New York (1978)
Doğandağ, S., Ferraris, P., Lifschitz, V.: Almost definite causal theories. In: Lifschitz, V., Niemelä, I. (eds.) LPNMR 2004. LNCS (LNAI), vol. 2923, pp. 74–86. Springer, Heidelberg (2003)
Giunchiglia, E., Lee, J., Lifschitz, V., McCain, N., Turner, H.: Nonmonotonic causal theories. Artificial Intelligence (2003) (to appear), http://www.cs.utexas.edu/users/vl/papers/nmct.ps
Lee, J., Lifschitz, V.: Describing additive fluents in action language C+. In: Proc. IJCAI 2003, pp. 1079–1084 (2003), http://www.cs.utexas.edu/users/appsmurf/papers/additive-ijcai.ps
Lee, J., Lifschitz, V.: Loop formulas for disjunctive logic programs. In: Palamidessi, C. (ed.) ICLP 2003. LNCS, vol. 2916, pp. 451–465. Springer, Heidelberg (2003) (to appear), http://www.cs.utexas.edu/users/appsmurf/papers/disjunctive.ps
Lifschitz, V., Tang, L.R., Turner, H.: Nested expressions in logic programs. Annals of Mathematics and Artificial Intelligence 25, 369–389 (1999)
Lifschitz, V., McCain, N., Remolina, E., Tacchella, A.: Getting to the airport: The oldest planning problem in AI. In: Minker, J. (ed.) Logic-Based Artificial Intelligence, pp. 147–165. Kluwer, Dordrecht (2000)
Lifschitz, V.: Missionaries and cannibals in the Causal Calculator. In: Principles of Knowledge Representation and Reasoning: Proc. Seventh Int’l. Conf., pp. 85–96 (2000)
Lin, F., Zhao, Y.: ASSAT: Computing answer sets of a logic program by SAT solvers. In: Proc. AAAI 2002 (2002)
McCain, N., Turner, H.: Causal theories of action and change. In: Proc. AAAI 1997, pp. 460–465 (1997)
McCain, N.: Causality in Commonsense Reasoning about Actions. PhD thesis, University of Texas at Austin (1997), ftp://ftp.cs.utexas.edu/pub/techreports/tr97-25.ps.Z
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lee, J. (2003). Nondefinite vs. Definite Causal Theories . In: Lifschitz, V., Niemelä, I. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2004. Lecture Notes in Computer Science(), vol 2923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24609-1_14
Download citation
DOI: https://doi.org/10.1007/978-3-540-24609-1_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20721-4
Online ISBN: 978-3-540-24609-1
eBook Packages: Springer Book Archive