A note on situation calculus

Authors

  • Antonios Paraskevas * Department of Applied Informatics, School of Information Sciences, University of Macedonia, Information Systems and e Business Laboratory (ISeB),156, Egnatia Str., 54636, Thessaloniki, Greece. https://orcid.org/0009-0003-4342-468X

https://doi.org/10.48313/uda.v1i1.22

Abstract

Situation calculus is a logical language for expressing change. Situations, actions, and fluents are the three core ideas of situation calculus. As agents perform actions, the dynamic environment changes from one situation to another. Fluents are functions that change with the situation and describe the effects of actions. They can be seen as properties of the world that come into existence when an action is initiated and disappear when another action ends. While situation calculus is powerful, it often struggles with complexity and verbosity when modeling dynamic systems, making it challenging to manage and reason about in large-scale settings. We propose using Labelled Transition Systems (LTS) to address these limitations. The LTS model, based on graph models of modal logic, offers a more concise and formal representation of system behaviors. The LTS-based method aims to provide a simpler and more intuitive framework for modeling dynamic settings, thereby improving system representation clarity and efficiency. It allows for higher scalability and more efficient verification and validation processes, which are critical in complex systems. Finally, the LTS model seeks to bridge the theoretical expressiveness of situation calculus with the practical requirements of system design and analysis.

Keywords:

Situation calculus , LTS model , Modal logic, Knowledge representation

References

  1. [1] McCarthy, j, & Hayes, P. (1969). Some philosophical problems from standpoint of artificial intelligence. In Readings in artificial intelligence (pp. 463–502). Elsevier. https://www-formal.stanford.edu/jmc/mcchay69.pdf

  2. [2] Farinelli, A., Finzi, A., & Lukasiewicz, T. (2007). Team programming in golog under partial observability. IJCAI international joint conference on artificial intelligence, 6(12), 2097–2102. https://ora.ox.ac.uk/objects/uuid:223b5f93-19c2-4a74-8e5f-149db676b09d

  3. [3] Ferrein, A., Fritz, C., & Lakemeyer, G. (2005). Using golog for deliberation and team coordination in robotic soccer. AI - artificial intelligence, 19(1), 24–31. https://www.cs.toronto.edu/~fritz/publications/200506061855_Ferrein2005Using.pdf

  4. [4] Ghaderi, H., Levesque, H., & Lespérance, Y. (2007). Towards a logical theory of coordination and joint ability. Proceedings of the international conference on autonomous agents (pp. 544–546). Association for Computing Machinery. https://doi.org/10.1145/1329125.1329223

  5. [5] Reiter, R. (1991). The frame problem in the situation calculus: A simple solution (sometimes) and a completeness result for goal regression. Artificial and mathematical theory of computation, 3, 359–380. https://doi.org/10.1016/b978-0-12-450010-5.50026-8

  6. [6] Sardina, S., De Giacomo, G., Lespérance, Y., & Levesque, H. J. (2004). On the semantics of deliberation in IndiGolog - From theory to implementation. Annals of mathematics and artificial intelligence, 41(2–4), 259–299. https://doi.org/10.1023/B:AMAI.0000031197.13122.aa

  7. [7] Scherl, R. B. (2022). A situation-calculus model of knowledge and belief based on thinking about justifications. CEUR workshop proceedings, 3197, 104–114. https://ceur-ws.org/Vol-3197/paper10.pdf

  8. [8] De Giacomo, G., Felli, P., Logan, B., Patrizi, F., & Sardiña, S. (2022). Situation calculus for controller synthesis in manufacturing systems with first-order state representation (extended abstract). IJCAI international joint conference on artificial intelligence (pp. 5722–5726). Elsevier. https://doi.org/10.24963/ijcai.2022/798

  9. [9] De Giacomo, G., Ternovska, E., & Reiter, R. (2020). Non-terminating processes in the situation calculus. Annals of mathematics and artificial intelligence, 88(5–6), 623–640. https://doi.org/10.1007/s10472-019-09643-9

  10. [10] Baier, J. A., & McIlraith, S. A. (2022). Knowledge-based programs as building blocks for planning. Artificial intelligence, 303, 103634. https://doi.org/10.1016/j.artint.2021.103634

  11. [11] Knight, S., Mardare, R., & Panangaden, P. (2011). An epistemic logic for labelled transition systems. McGill University. https://www.cs.mcgill.ca/~prakash/Pubs/completeness_paper.pdf

  12. [12] Tretmans, J. (2008). Model based testing with labelled transition systems. In Lecture notes in computer science (Vol. 4949 LNCS, pp. 1–38). Springer. https://doi.org/10.1007/978-3-540-78917-8_1

  13. [13] Baier, C., & Katoen, J. P. (2008). Principles of model checking (Vol. 950). MIT Press.

  14. [14] Giannakopoulou, D., & Magee, J. (2003). Fluent model checking for event-based systems. Proceedings of the acm sigsoft symposium on the foundations of software engineering (pp. 257–266). IEEE. https://doi.org/10.1145/940071.940106

  15. [15] Hughes, G. E., & Cresswell, M. J. (2012). A new introduction to modal logic. Routledge.

  16. [16] Zadeh, L. A. (2014). A note on modal logic and possibility theory. Information sciences, 279, 908–913. https://doi.org/10.1016/j.ins.2014.04.002

  17. [17] Russell, S., & Norvig, P. (2020). Artificial intelligence: A modern approach. Pearson.

Published

2024-06-15

How to Cite

Paraskevas, A. (2024). A note on situation calculus. Uncertainty Discourse and Applications, 1(1), 66-72. https://doi.org/10.48313/uda.v1i1.22

Similar Articles

1-10 of 26

You may also start an advanced similarity search for this article.