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A Family of Dynamic Description Logics for Representing and Reasoning About Actions

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Abstract

Description logics provide powerful languages for representing and reasoning about knowledge of static application domains. The main strength of description logics is that they offer considerable expressive power going far beyond propositional logic, while reasoning is still decidable. There is a demand to bring the power and character of description logics into the description and reasoning of dynamic application domains which are characterized by actions. In this paper, based on a combination of the propositional dynamic logic PDL, a family of description logics and an action formalism constructed over description logics, we propose a family of dynamic description logics DDL(X @) for representing and reasoning about actions, where X represents well-studied description logics ranging from the to the , and X @ denotes the extension of X with the @ constructor. The representation power of DDL(X @) is reflected in four aspects. Firstly, the static knowledge of application domains is represented as RBoxes and acyclic TBoxes of the description logic X. Secondly, the states of the world and the pre-conditions of atomic actions are described by ABox assertions of the description logic X @, and the post-conditions of atomic actions are described by primitive literals of X @. Thirdly, starting with atomic actions and ABox assertions of X @, complex actions are constructed with regular program constructors of PDL, so that various control structures on actions such as the “Sequence”, “Choice”, “Any-Order”, “Iterate”, “If-Then-Else”, “Repeat-While” and “Repeat-Until” can be represented. Finally, both atomic actions and complex actions are used as modal operators for the construction of formulas, so that many properties on actions can be explicitly stated by formulas. A tableau-algorithm is provided for deciding the satisfiability of DDL(X @)-formulas; based on this algorithm, reasoning tasks such as the realizability, executability and projection of actions can be effectively carried out. As a result, DDL(X @) not only offers considerable expressive power going beyond many action formalisms which are propositional, but also provides decidable reasoning services for actions described by it.

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References

  1. Areces, C., Blackburn, P., Marx, M.: A roadmap on complexity for hybrid logics. In: Proc. of the 13th Int’l Workshop and 8th Annual Conf. of the EACSL on Computer Science Logic (CSL’05). LNCS, vol. 1683, pp. 307–321. Springer (1999)

  2. Artale, A., Franconi, E.: A temporal description logic for reasoning about actions and plans. J. Artif. Intell. Res. 9, 463–506 (1998)

    MathSciNet  MATH  Google Scholar 

  3. Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F.: The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  4. Baader, F., Lutz, C., Miličić, M., Sattler, U., Wolter., F.: Integrating description logics and action formalisms: first results. In: Proc. of the 12th Nat. Conf. on Artificial Intelligence (AAAI’05), pp. 572–577. AAAI Press / MIT Press (2005)

  5. Berners-Lee, T., Hendler, J., Lassila, O.: The semantic web. Sci. Am. 284(5), 34–43 (2001)

    Article  Google Scholar 

  6. Calvanese, D., De Giacomo, G., Vardi, M.: Reasoning about actions and planning in LTL action theories. In: Proc. of the 8th Int’l Conf. on Principles of Knowledge Representation and Reasoning (KR’02), pp. 593–602. AAAI Press (2002)

  7. Calvanese, D., De Giacomo, G., Lenzerini, M., Rosati, R.: Actions and programs over description logic ontologies. In: Proc. of the 20th Int’l Workshop on Description Logics (DL’07), pp. 29–40 (2007)

  8. Chang, L., Shi, Z., Qiu, L., Lin, F.: Dynamic description logic: embracing actions into description logic. In: Proc. of the 20th Int’l Workshop on Description Logics (DL’07), pp. 243–250 (2007)

  9. De Giacomo, G., Lenzerini, M.: PDL-based framework for reasoning about actions. In: Proc. of the 4th Congresss of the Italian Association for Artificial Intelligence (AI*IA’95), pp. 103–114. Springer, Berlin (1995)

    Google Scholar 

  10. De Giacomo, G., Massacci, F.: Tableaux and algorithms for propositional dynamic logic with converse. In: Proc. of the 13th Int’l Conf. on Automated Deduction (CADE’96), pp. 613–628. Springer, Berlin (1996)

    Chapter  Google Scholar 

  11. Devanbu, P.T., Litman, D.J.: Taxonomic plan reasoning. Artif. Intell. 84(1–2), 1–35 (1996)

    Article  Google Scholar 

  12. Drescher, C., Thielscher, M.: Integrating action calculi and description logics. In: Proc. of the 30th Annual German Conf. on Artificial Intelligence (KI’07), pp. 68–83. Springer, Berlin (2007)

    Google Scholar 

  13. Fikes, R.E., Hart, P.E., Nilsson, N.J.: Learning and executing generalized robot plans. Artif. Intell. 3, 251–288 (1972)

    Article  Google Scholar 

  14. Fischer M.J., Ladner, R.E.: Propositional modal logic of programs: extended abstract. In: Proc. of the 9th Annual ACM Symposium on Theory of Computing (STOC’77), pp. 286–294 (1977)

  15. Fischer M.J., Ladner, R.E.: Propositional dynamic logic of regular programs. J. Comput. Syst. Sci. 18(2), 194–211 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  16. Giordano, L., Martelli, A., Schwind, C.: Reasoning about actions in dynamic linear time temporal logic. Logic J. IGPL 9(3), 79–92 (2001)

    MathSciNet  Google Scholar 

  17. Grädel E., Otto, M., Rosen, E.: Two-variable logic with counting is decidable. In: Proc. of the 12th Annual IEEE Symposium on Logic in Computer Science (LICS’97), pp. 306–317. IEEE Computer Society Press, Los Alamitos (1997)

    Google Scholar 

  18. Gu, Y., Soutchanski, M.: A logic for decidable reasoning about services. In: Proc. of AAAI-06 workshop on AI Driven Technologies for Services-Oriented Computing (2006)

  19. Gu, Y., Soutchanski, M.: Decidable reasoning in a modified situation calculus. In: Proc. of the 12th Int’l Joint Conf. on Artificial Intelligence (IJCAI’07), pp. 1891–1897. Morgan Kaufmann Publishers, San Fransisco (2007)

    Google Scholar 

  20. Heinsohn, J., Kudenko, D., Nebel, B., Profitlich, H.J.: Rat—representation of actions using terminological logics. In: Proc. of the DFKI Workshop on Taxonomic Reasoning, Technical Report D-92-08, DFKI, Saarbrüken (1992)

  21. Horrocks, I., Patel-Schneider, P.F., Harmelen, F.V.: From SHIQ and RDF to OWL: the making of a web ontology language. J. Web Semant. 1(1), 7–26 (2003)

    Article  MATH  Google Scholar 

  22. Horrocks, I., Sattler, U.: A tableaux decision procedure for SHOIQ. J. Autom. Reason. 39(3), 249–276 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  23. Liu, H., Lutz, C., Miličić, M., Wolter, F.: Updating description logic ABoxes. In: Proc. of the 10th Int’l Conf. on Principles of Knowledge Representation and Reasoning (KR’06), pp. 46–56. AAAI Press, California (2006)

    Google Scholar 

  24. Liu, H., Lutz, C., Miličić, M., Wolter, F.: Reasoning about actions using description logics with general TBoxes. In: Proc. of the 10th European Conf. on Logics in Artificial Intelligence (JELIA’06), pp. 266–279. Springer (2006)

  25. Liu, H.: Computing updates in description logics. Ph.D. thesis, Technischen Universität Dresden (2010)

  26. Lutz, C., Sattler, U.: A proposal for describing services with DLs. In: Proc. of the 15th Int’l Workshop on Description Logics (DL’02) (2002)

  27. Martin, D., Burstein, M., McDermott, D., McIlraith, S., Paolucci, M., Sycara, K., McGuinness, D., Sirin, E., Srinivasan, N.: Bringing semantics to web services with OWL-S. World Wide Web J. 10(3), 243–277 (2007)

    Article  Google Scholar 

  28. McCarthy, J., Hayes, P.: Some philosophical problems form the standpoint of artificaial intelligence. Mach. Intell. 4, 463–502 (1969)

    MATH  Google Scholar 

  29. McIlraith, S., Son, T., Zeng, H.: Semantic web services. IEEE Intell. Syst. 16(2), 46–53 (2001)

    Article  Google Scholar 

  30. Miličić, M.: Planning in action formalisms based on DLs: first results. In: Proc. of the 20th Int’l Workshop on Description Logics (DL’07), pp. 112–122 (2007)

  31. Miličić, M: Complexity of planning in action formalisms based on description logics. In: Proc. of the 14th Int’l Conf. on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR’07), pp. 408–422 (2007)

  32. Myers, R., Pattinson, D., Schrǒder, L.: Coalgebraic hybrid logic. In: Proc. of the 12th Int’l Conf. on Foundations of Software Science and Computational Structures (FoSSaCS’09), pp. 137–151 (2009)

  33. Narayanan, S., McIlraith, S.: Simulation, verification and automated composition of web services. In: Proc. of the 11th Int’l World Wide Web Conference (WWW’02), pp. 77–88 (2002)

  34. Pacholski, L., Szwast, W., Tendera, L.: Complexity of two-variable logic with counting. In: Proc. of the 12th Annual IEEE Symposium on Logic in Computer Science (LICS’97), pp. 318–327. IEEE Computer Society Press, Los Alamitos (1997)

    Google Scholar 

  35. Pratt, V.R.: A practical decision method for propositional dynamic logic. In: Proc. of the 10th Annual ACM Symposium on Theory of Computing (STOC’78), pp. 326–337 (1978)

  36. Reiter, R.: Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems. MIT Press, Cambridge, MA (2001)

    MATH  Google Scholar 

  37. Schmidt-Schauß, M., Smolka, G.: Attributive concept descriptions with complements. Artif. Intell. 48(1), 1–26 (1991)

    Article  MATH  Google Scholar 

  38. Shi, Z., Dong, M., Jiang, Y., Zhang, H.: A logic foundation for the semantic web. Sci. China Ser. F 48(2), 161–178 (2005)

    Article  Google Scholar 

  39. Smith, M.K., Welty, C., McGuinness D.L.: OWL web ontology language guide. W3C Recommendation, 10 Feb. 2004. http://www.w3.org/TR/owl-guide/. Accessed 3 Jan 2009

  40. Thielscher, M.: From situation calculus to fluent calculus: state update axioms as a solution to the inferential frame problem. Artif. Intell. 111(1–2), 277–299 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  41. Tobies, S.: The complexity of reasoning with cardinality restrictions and nominals in expressive description logics. J. Artif. Intell. Res. 12(1), 199–217 (2000)

    MathSciNet  MATH  Google Scholar 

  42. Wolter, F., Zakharyaschev, M.: Satisfiability problem in description logics with modal operators. In: Proc. of the 6th Int’l Conf. on Principles of Knowledge Representation and Reasoning (KR’98), pp. 512–523. Morgan Kaufmann Publishers, San Francisco (1998)

    Google Scholar 

  43. Wolter, F., Zakharyaschev, M.: Dynamic description logic. Adv. Modal Log. 2, 449–463 (2000)

    Google Scholar 

  44. Zolin, E.: Complexity of reasoning in description logics. http://www.cs.man.ac.uk/~ezolin/dl/. Accessed 10 Jan 2010

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Authors and Affiliations

  1. School of Computer and Control, Guilin University of Electronic Technology, Guilin, 541004, China

    Liang Chang, Tianlong Gu & Lingzhong Zhao

  2. State Key Lab. of Software Engineering, Computer School, Wuhan University, Wuhan, 430072, China

    Liang Chang

  3. Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, P.O. Box 2704-28, Beijing, 100080, China

    Zhongzhi Shi

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  1. Liang Chang
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  2. Zhongzhi Shi
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  3. Tianlong Gu
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  4. Lingzhong Zhao
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Correspondence to Liang Chang.

Additional information

This work was partially supported by the National Natural Science Foundation of China (Nos. 60903079, 60775035, 60963010, 60803033, 61035003), the National Basic Research Program of China (No. 2007CB311004), the State Key Laboratory of Software Engineering (SKLSE) and the 111 Project (No. B07037).

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Chang, L., Shi, Z., Gu, T. et al. A Family of Dynamic Description Logics for Representing and Reasoning About Actions . J Autom Reasoning 49, 1–52 (2012). https://doi.org/10.1007/s10817-010-9210-1

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