Skip to main content

The Aspect Calculus

  • Conference paper
  • First Online:
Book cover Automated Deduction – CADE 27 (CADE 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11716))

Included in the following conference series:

  • 616 Accesses

Abstract

For theorem proving applications, the aspect calculus for reasoning about states and actions has some advantages over existing situation calculus formalisms, and also provides an application domain and a source of problems for first-order theorem provers. The aspect calculus provides a representation for reasoning about states and actions that is suited to modular domains. An aspect names a portion of a state, that is, a substate, such as a room in a building or a city in a country. Aspects may have aspects of their own. A state is assumed to be either a leaf state that cannot be further decomposed, or to be composed of substates, and actions associated with one substate do not influence other, disjoint substates. This feature can reduce the number of frame axioms that are needed if the domain has a modular structure. It can also permit planning problems on independent substates to be solved independently to some degree. However, interactions between independent substates are also permitted.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Davis, E.: Representations of Commonsense Knowledge. Morgan Kaufmann, Burlington (1990)

    Google Scholar 

  2. Denecker, M., Ternovska, E.: Inductive situation calculus. Artif. Intell. 171(5–6), 332–360 (2007)

    Article  MathSciNet  Google Scholar 

  3. Haas, A.R.: The case for domain-specic frame axioms. In: Brown, F.M. (ed.) The Frame Problem in Artificial Intelligence, Proceedings of the 1987 Workshop, pp. 343–348. Morgan Kaufmann (1987)

    Google Scholar 

  4. Hayes, P.: The frame problem and related problems in artificial intelligence. In: Elithorn, A., Jones, D. (eds.) Artificial and Human Thinking, pp. 45–59. Jossey-Bass Inc., Elsevier Scientific Publishing Company, San Francisco, Amsterdam (1973)

    Google Scholar 

  5. Lin, F.: Situation calculus. In: van Harmelen, F., Lifschitz, V., Porter, B. (eds.) Handbook of Knowledge Representation, pp. 649–669. Elsevier, Amsterdam (2008)

    Chapter  Google Scholar 

  6. Lin, F., Reiter, R.: State constraints revisited. J. Logic Comput. 4(5), 655–678 (1994)

    Article  MathSciNet  Google Scholar 

  7. McIlraith, S.A.: Integrating actions and state constraints: a closed-form solution to the ramification problem (sometimes). Artif. Intell. 116(1), 87–121 (2000)

    Article  MathSciNet  Google Scholar 

  8. McCarthy, J., Hayes, P.: Some philosophical problems from the standpoint of artificial intelligence. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence 4, pp. 463–502. Edinburgh University Press, Edinburgh (1969)

    MATH  Google Scholar 

  9. Matos, P.A., Martins, J.P.: Contextual logic of change and the ramification problem. In: Coasta, E., Cardoso, A. (eds.) EPIA 1997. LNCS, vol. 1323, pp. 267–278. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0023928

    Chapter  Google Scholar 

  10. Pednault, E.P.D.: ADL: exploring the middle ground between STRIPS and the situation calculus. In: Proceedings of the International Conference on Principles of Knowledge Representation (KR-1998), pp. 324–332. Morgan Kaufmann Inc. (1989)

    Google Scholar 

  11. Petrick, R.P.A.: Cartesian situations and knowledge decomposition in the situation calculus. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Eleventh International Conference, KR 2008, Sydney, Australia, 16–19 September 2008, pp. 629–639 (2008)

    Google Scholar 

  12. Reiter, R.: The frame problem in the situation calculus: a simple solution (sometimes) and a completeness result for goal regression. In: Lifschitz, V. (ed.) Artificial Intelligence and Mathematical Theory of Computation: Papers in Honor of John McCarthy, pp. 359–380. Academic Press, Cambridge (1991)

    Chapter  Google Scholar 

  13. Schubert, L.: Monotonic solution of the frame problem in the situation calculus: an efficient method for worlds with fully specified actions. In: Kyburg, H.E., Loui, R.P., Carlson, G.N. (eds.) Knowledge Representation and Defeasible Reasoning, vol. 5, pp. 23–67. Kluwer Academic Publishers, Dordrecht (1990)

    Chapter  Google Scholar 

  14. Shanahan, M.: The ramification problem in the event calculus. In: Proceedings of the 16th International Joint Conference on Artifical Intelligence - Volume 1, IJCAI 1999, pp. 140–146. Morgan Kaufmann Publishers Inc., San Francisco (1999)

    Google Scholar 

  15. Scherl, R.B., Levesque, H.J.: The frame problem and knowledge-producing actions. In: Proceedings of the Eleventh National Conference on Artificial Intelligence (AAAI-1993), Washington, D.C., USA, pp. 689–697. AAAI Press/MIT Press (1993)

    Google Scholar 

  16. Ternovska, E.: Id-logic and the ramification problem for the situation calculus. In: ECAI (2000)

    Google Scholar 

  17. Thielscher, M.: Introduction to the fluent calculus. Electron. Trans. Artif. Intell. 2, 179–192 (1998)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to David A. Plaisted .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Plaisted, D.A. (2019). The Aspect Calculus. In: Fontaine, P. (eds) Automated Deduction – CADE 27. CADE 2019. Lecture Notes in Computer Science(), vol 11716. Springer, Cham. https://doi.org/10.1007/978-3-030-29436-6_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-29436-6_24

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-29435-9

  • Online ISBN: 978-3-030-29436-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics