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Reformulating Action Language \(\mathcal{C}\)+ in Answer Set Programming

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7265))

Abstract

Action language \(\mathcal{C}\)+ is a high level notation of nonmonotonic causal logic for describing properties of actions. The definite fragment of \(\mathcal{C}\)+ is implemented in Version 2 of the Causal Calculator (CCalc) based on the reduction of nonmonotonic causal logic to propositional logic. On the other hand, here we present two reformulations of the definite fragment of \(\mathcal{C}\)+ in terms of different versions of the stable model semantics. The first reformulation is in terms of the recently proposed stable model semantics of formulas with intensional functions, and can be encoded in the input language of CSP solvers. The second reformulation is in terms of the stable model semantics of propositional logic programs, which can be encoded in the input language of ASP systems. The second one is obtained from the first one by eliminating intensional functions in favor of intensional predicates.

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References

  1. Giunchiglia, E., Lee, J., Lifschitz, V., McCain, N., Turner, H.: Nonmonotonic causal theories. Artificial Intelligence 153(1–2), 49–104 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Giunchiglia, E., Lifschitz, V.: An action language based on causal explanation: Preliminary report. In: Proceedings of National Conference on Artificial Intelligence (AAAI), pp. 623–630. AAAI Press (1998)

    Google Scholar 

  3. 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.gz

  4. Lee, J.: Automated Reasoning about Actions. PhD thesis, University of Texas at Austin (2005), http://peace.eas.asu.edu/joolee/papers/dissertation.pdf

  5. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R., Bowen, K. (eds.) Proceedings of International Logic Programming Conference and Symposium, pp. 1070–1080. MIT Press (1988)

    Google Scholar 

  6. Gelfond, M., Lifschitz, V.: Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385 (1991)

    Article  MATH  Google Scholar 

  7. Ferraris, P., Lee, J., Lierler, Y., Lifschitz, V., Yang, F.: Representing first-order causal theories by logic programs. Theory and Practice of Logic Programming (2011), Available on CJO 2011, doi:10.1017/S1471068411000081

    Google Scholar 

  8. Casolary, M., Lee, J.: Representing the language of the causal calculator in answer set programming. In: ICLP (Technical Communications), pp. 51–61 (2011)

    Google Scholar 

  9. Bartholomew, M., Lee, J.: Stable models of formulas with intensional functions. In: Proceedings of International Conference on Principles of Knowledge Representation and Reasoning, KR (to appear, 2012)

    Google Scholar 

  10. Ferraris, P.: Answer Sets for Propositional Theories. In: Baral, C., Greco, G., Leone, N., Terracina, G. (eds.) LPNMR 2005. LNCS (LNAI), vol. 3662, pp. 119–131. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  11. Clark, K.: Negation as failure. In: Gallaire, H., Minker, J. (eds.) Logic and Data Bases, pp. 293–322. Plenum Press, New York (1978)

    Chapter  Google Scholar 

  12. Simons, P., Niemelä, I., Soininen, T.: Extending and implementing the stable model semantics. Artificial Intelligence 138, 181–234 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lee, J., Palla, R.: System f2lp – Computing Answer Sets of First-Order Formulas. In: Erdem, E., Lin, F., Schaub, T. (eds.) LPNMR 2009. LNCS, vol. 5753, pp. 515–521. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  14. Ferraris, P., Lee, J., Lifschitz, V.: A new perspective on stable models. In: Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), pp. 372–379 (2007)

    Google Scholar 

  15. Ferraris, P., Lee, J., Lifschitz, V.: Stable models and circumscription. Artificial Intelligence 175, 236–263 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. Gelfond, M., Lifschitz, V.: Action languages. Electronic Transactions on Artificial Intelligence 3, 195–210 (1998), http://www.ep.liu.se/ea/cis/1998/016/

    Google Scholar 

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Lee, J. (2012). Reformulating Action Language \(\mathcal{C}\)+ in Answer Set Programming. In: Erdem, E., Lee, J., Lierler, Y., Pearce, D. (eds) Correct Reasoning. Lecture Notes in Computer Science, vol 7265. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30743-0_28

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  • DOI: https://doi.org/10.1007/978-3-642-30743-0_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30742-3

  • Online ISBN: 978-3-642-30743-0

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