Knowledge, Proof and Dynamics pp 73-96 | Cite as

# Local Fact Change Logic

- 8 Downloads

## Abstract

We investigate a modal logic of model change, introducing a new operator which allows for changing the valuation at a particular state in a model. After investigating some properties of the logic, and aspects of its expressive power, we show it to be undecidable by way of a reduction using memory logic.

## Notes

### Acknowledgements

I would like to thank Carlos Areces for very helpful input, especially in connection with memory logics. Ben Sparkes encouraged investigating similarities with hybrid logics, which led to many of the results in this paper. I also received very helpful feedback from Johan van Benthem, the members of the Logic Workshop at Stanford, and the participants of the Fourth Asian Workshop in Philosophical Logic. Finally, the anonymous reviewers provided very useful feedback.

## References

- Areces, Carlos, Raul Fervari, Guillaume Hoffmann, and Mauricio Martel. 2017. Undecidability of Relation-Changing Modal Logics. In
*Dynamic Logic. New Trends and Applications*, vol. 23, 1–16. Lecture Notes in Computer Science. Cham: Springer. ISBN: 978-3-319-73578-8 978-3- 319-73579-5.Google Scholar - Areces, Carlos. 2007. Hybrid Logics: The Old and The New. In
*Proceedings of LogKCA-07*, 15–29.Google Scholar - Areces, Carlos, Diego Figueira, Santiago Figueira, and Sergio Mera. 2011. The Expressive Power of Memory Logics.
*The Review of Symbolic Logic*4 (02): 290–318.CrossRefGoogle Scholar - Aucher, Guillaume, Philippe Balbiani, Luis Fariñas del Cerro, and Andreas Herzig. 2009. Global and Local Graph Modifiers.
*Electronic Notes in Theoretical Computer Science*231(25): 293–307; In*Proceedings of the 5th Workshop on Methods for Modalities (M4M5 2007)*.Google Scholar - Aucher, Guillaume, Johan van Benthem, and Davide Grossi. 2018. Modal Logics of Sabotage Revisited.
*Journal of Logic and Computation*28 (2): 269–303.CrossRefGoogle Scholar - Balbiani, Philippe, Andreas Herzig, and Nicolas Troquard. 2013. Dynamic Logic of Propositional Assignments: A Well-Behaved Variant of PDL. In
*Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science*, 143–152. LICS ’13. Washington: IEEE Computer Society. ISBN: 978-0-7695-5020-6.Google Scholar - Benthem, van, and Johan. 1997. Modal Foundations for Predicate Logic.
*Logic Journal of the IGPL*5: 259–286.Google Scholar - Benthem, van, Patrick Girard Johan, and Olivier Roy. 2009. Everything Else Being Equal: A Modal Logic for Ceteris Paribus Preferences.
*Journal of Philosophical Logic*38 (1): 83–125.Google Scholar - Blackburn, Patrick, and Jerry Seligman. 1995. Hybrid Languages.
*Journal of Logic, Language and Information*4 (3): 251–272.CrossRefGoogle Scholar - Bockmayr, Alexander, and Heike Siebert. 2013. Bio-Logics: Logical Analysis of Bioregulatory Networks. In
*Programming Logics*, vol. 7797, eds. Andrei Voronkov and Christoph Weidenbach, 19-34. Berlin: Springer. ISBN: 978-3-642-37650-4 978-3-642-37651-1.Google Scholar - de Bruin, B.P. 2004.
*Explaining Games: On the Logic of Game Theoretic Explanations*. Amsterdam: Institute for Logic, Language and Computation. ISBN: 978-90-5776-129-4.Google Scholar - der Hoek, Van, and Wiebe, and Michael Wooldridge. 2005. On the Logic of Cooperation and Propositional Control.
*Artificial Intelligence*164(1–2): 81–119.Google Scholar - Gutierrez, Julian, Paul Harrenstein, and Michael Wooldridge. 2015. Iterated Boolean Games.
*Information and Computation*242: 53–79.CrossRefGoogle Scholar - Harrenstein, Paul, Wiebe van der Hoek, John-Jules Meyer, and Cees Witteveen. 2001. Boolean Games. In
*Proceedings of the 8th Conference on Theoretical Aspects of Rationality and Knowledge*, 287–298. Burlington: Morgan Kaufmann Publishers Inc.Google Scholar - Harrenstein, Paul, Wiebe Van der Hoek, John-Jules Meyer, and Cees Witteveen. 2003. A Modal Characterization of Nash Equilibrium.
*Fundamenta Informaticae*57(2-4): 281–321.Google Scholar - Mera, Sergio Fernando. 2009. Modal Memory Logics. PhD Thesis, Universidad de Buenos Aires.Google Scholar
- Miller, Joseph S., and Lawrence S. Moss. 2005. The Undecidability of Iterated Modal Relativization.
*Studia Logica*79, no. 3 (1): 373–407.Google Scholar - Seligman, Jeremy, and Declan Thompson. 2015. Boolean Network Games and Iterated Boolean Games. In
*Logic, Rationality, and Interaction*, eds. Wiebe van der Hoek, Wesley H. Holliday, and Wen-fang Wang, 353–365. Lecture Notes in Computer Science. Berlin: Springer. ISBN: 978-3-662-48561-3.Google Scholar - Tiomkin, M.L., and J.A. Makowsky. 1985. Propositional Dynamic Logic with Local Assignment.
*Theoretical Computer Science*36 (1): 71–87.CrossRefGoogle Scholar - van Benthem, Johan. 2011.
*Logical Dynamics of Information and Interaction*. Cambridge: Cambridge University Press. ISBN: 978-0-521-76579-4.Google Scholar - van Benthem, Johan. 2018. Constructive Agents.
*Indagationes Mathematicae*29(1): 23–35.Google Scholar