Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
157 tokens/sec
GPT-4o
43 tokens/sec
Gemini 2.5 Pro Pro
43 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
47 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

An Abstract Look at Awareness Models and Their Dynamics (2307.05049v1)

Published 11 Jul 2023 in cs.LO

Abstract: This work builds upon a well-established research tradition on modal logics of awareness. One of its aims is to export tools and techniques to other areas within modal logic. To this end, we illustrate a number of significant bridges with abstract argumentation, justification logics, the epistemic logic of knowing-what and deontic logic, where basic notions and definitional concepts can be expressed in terms of the awareness operator combined with the box modality. Furthermore, these conceptual links point to interesting properties of awareness sets beyond those standardly assumed in awareness logics, i.e. positive and negative introspection. We show that the properties we list are characterised by corresponding canonical formulas, so as to obtain a series of off-the-shelf axiomatisations for them. As a second focus, we investigate the general dynamics of this framework by means of event models. Of specific interest in this context is to know under which conditions, given a model that satisfies some property, the update with an event model keeps it within the intended class. This is known as the closure problem in general dynamic epistemic logics. As a main contribution, we prove a number of closure theorems providing sufficient conditions for the preservation of our properties. Again, these results enable us to axiomatize our dynamic logics by means of reduction axioms.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (40)
  1. Alan Ross Anderson (1958): A reduction of deontic logic to alethic modal logic. Mind 67(265), pp. 100–103, 10.1093/mind/LXVII.265.100.
  2. Sergei Artemov & Melvin Fitting (2016): Justification Logic. In Edward N. Zalta, editor: The Stanford Encyclopedia of Philosophy, Metaphysics Research Lab, Stanford University.
  3. Guillaume Aucher (2008): Consistency preservation and crazy formulas in BMS. In S. Hölldobler, C. Lutz & H. Wansing, editors: European Workshop on Logics in Artificial Intelligence, LNCS 5293, Springer, pp. 21–33, 10.1007/978-3-540-87803-24.
  4. In T. Bolander, T. Braüner, S. Ghilardi, & L. Moss, editors: Advances in modal logic, 9, College Publication, pp. 36–54.
  5. Alexandru Baltag & Lawrence S Moss (2004): Logics for epistemic programs. Synthese 139(2), pp. 165–224, 10.1023/B:SYNT.0000024912.56773.5e.
  6. In I. Gilboa, editor: Proceedings of the 7th Conference on Theoretical Aspects of Rationality and Knowledge (TARK), Morgan Kaufmann Publishers, pp. 43–56, 10.1007/978-3-319-20451-238.
  7. Alexandru Baltag & Bryan Renne (2016): Dynamic Epistemic Logic. In Edward N. Zalta, editor: The Stanford Encyclopedia of Philosophy, Winter 2016 edition, Metaphysics Research Lab, Stanford University.
  8. Alexandru Baltag & Sonja Smets (2008): A qualitative theory of dynamic interactive belief revision. In Wiebe van der Hoek, Giacomo Bonanno & Michael Wooldridge, editors: Logic and the foundations of game and decision theory (LOFT 7), Texts in Logic and Games 3, Amsterdam University Press, pp. 9–58, 10.1007/978-3-319-20451-239.
  9. Johan van Benthem (2011): Logical dynamics of information and interaction. Cambridge University Press, 10.1017/CBO9780511974533.
  10. Johan van Benthem, Jan van Eijck & Barteld Kooi (2006): Logics of communication and change. Information and computation 204(11), pp. 1620–1662, 10.1016/j.ic.2006.04.006.
  11. Johan van Benthem & Fernando R Velázquez-Quesada (2010): The dynamics of awareness. Synthese 177(1), pp. 5–27, 10.1007/s11229-010-9764-9.
  12. Patrick Blackburn, Maarten De Rijke & Yde Venema (2002): Modal Logic. Cambridge University Press, 10.1017/CBO9781107050884.
  13. Alfredo Burrieza & Antonio Yuste-Ginel (2020): Basic beliefs and argument-based beliefs in awareness epistemic logic with structured arguments. In Henry Prakken, Stefano Bistarelli, Francesco Santini & Carlo Taticchi, editors: Proceedings of the COMMA 2020, IOS Press, pp. 123–134, 10.3233/FAIA200498.
  14. Alfredo Burrieza & Antonio Yuste-Ginel (2021): An Awareness Epistemic Framework for Belief, Argumentation and Their Dynamics. In Joseph Y. Halpern & Andrés Perea, editors: Proceedings Eighteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK), EPTCS 335, pp. 69–83, 10.4204/EPTCS.335.6.
  15. Hans van Ditmarsch, Tim French & Fernando R. Velázquez-Quesada (2012): Action models for knowledge and awareness. In Wiebe van der Hoek, Lin Padgham, Vincent Conitzer & Michael Winikoff, editors: International Conference on Autonomous Agents and Multiagent Systems (AAMAS), IFAAMAS, pp. 1091–1098.
  16. In Burkhard C. Schipper, editor: Proceedings Eighteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK), 10.48550/arXiv.1310.6410.
  17. Hans van Ditmarsch, Wiebe van der Hoek & Barteld Kooi (2007): Dynamic epistemic logic. Springer, 10.1007/978-1-4020-5839-4.
  18. Hans van Ditmarsch & Barteld Kooi (2008): Semantic results for ontic and epistemic change. In Wiebe van der Hoek, Giacomo Bonanno & Michael Wooldridge, editors: Logic and the foundations of game and decision theory (LOFT 7), Texts in Logic and Games 3, Amsterdam University Press, pp. 9–58, 10.48550/arXiv.cs/0610093.
  19. Phan Minh Dung (1995): On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence 77(2), pp. 321–357, 10.1016/0004-3702(94)00041-X.
  20. Artificial intelligence 34(1), pp. 39–76, 10.1016/0004-3702(87)90003-8.
  21. Davide Grossi & Fernando R. Velázquez-Quesada (2015): Syntactic awareness in logical dynamics. Synthese 192(12), pp. 4071–4105, 10.1007/s11229-015-0733-1.
  22. Joseph Y Halpern (2001): Alternative semantics for unawareness. Games and Economic Behavior 37(2), pp. 321–339, 10.1006/game.2000.0832.
  23. Bengt Hansson (1969): An analysis of some deontic logics. Nous, pp. 373–398, 10.1007/978-94-010-3146-25.
  24. David Harel, Dexter Kozen & Jerzy Tiuryn (2001): Dynamic logic. In Dov M. Gabbay & Franz Guenthner, editors: Handbook of philosophical logic, 4, Springer, Dordrecht, pp. 99–217, 10.1007/978-94-017-0456-42.
  25. Aviad Heifetz, Martin Meier & Burkhard C Schipper (2006): Interactive unawareness. Journal of economic theory 130(1), pp. 78–94, 10.1016/j.jet.2005.02.007.
  26. Jaakko Hintikka (1962): Knowledge and belief: an introduction to the logic of the two notions. Cornell University Press.
  27. Addison-Wesley.
  28. Stig Kanger (1970): New foundations for ethical theory (1957). Reprinted. In . R Hilpinen, editor: Deontic logic: introductory and systematic readings, Springer, 10.1007/978-94-010-3146-22.
  29. Barteld Kooi (2007): Expressivity and completeness for public update logics via reduction axioms. Journal of Applied Non-Classical Logics 17(2), pp. 231–253, 10.3166/jancl.17.231-253.
  30. Sanjay Modgil & Henry Prakken (2013): A general account of argumentation with preferences. Artificial Intelligence 195, pp. 361–397, 10.1016/j.artint.2012.10.008.
  31. Jan Plaza (1989): Logics of public communications. In M.L. Emrich, M.S. Pfeifer, M. Hadzikadic & Z.W. Ras, editors: Proceedings 4th International Symposium on Methodologies for Intelligent Systems, Oak Ridge National Laboratory, pp. 201–216, 10.1007/s11229-007-9168-7.
  32. Carlo Proietti & Antonio Yuste-Ginel (2020): Persuasive Argumentation and Epistemic Attitudes. In Luís Soares Barbosa & Alexandru Baltag, editors: Dynamic Logic. New Trends and Applications, LNCS 12005, Springer, pp. 104–123, 10.1007/978-3-030-38808-97.
  33. Carlo Proietti & Antonio Yuste-Ginel (2021): Dynamic epistemic logics for abstract argumentation. Synthese 199(3-4), pp. 8641–8700, 10.1007/s11229-021-03178-5.
  34. Burkhard C. Schipper (2015): Awareness. In Hans van Ditmarsch, Joseph Y. Halpern, Wiebe van der Hoek & Barteld Kooi, editors: Handbook of Epistemic Logic, London: College Publications, pp. 77–146, 10.2139/ssrn.2401352.
  35. François Schwarzentruber, Srdjan Vesic & Tjitze Rienstra (2012): Building an Epistemic Logic for Argumentation. In Luis Fariñas del Cerro, Andreas Herzig & Jérôme Mengin, editors: Logics in Artificial Intelligence, LNCS 7519, Springer, pp. 359–371, 10.1007/978-3-642-33353-8_28.
  36. Matthias Thimm (2014): Strategic argumentation in multi-agent systems. KI-Künstliche Intelligenz 28(3), pp. 159–168, 10.1007/s13218-014-0307-2.
  37. Johan Van Benthem, Davide Grossi & Fenrong Liu (2014): Priority structures in deontic logic. Theoria 80(2), pp. 116–152, 10.1111/theo.12028.
  38. Fernando Raymundo Velázquez-Quesada (2010): Small steps in dynamics of information. Ph.D. thesis, Institute for Logic, Language and Computation, Universiteit van Amsterdam.
  39. Yanjing Wang (2018): Beyond Knowing That: A New Generation of Epistemic Logics. In Hans van Ditmarsch & Gabriel Sandu, editors: Jaakko Hintikka on Knowledge and Game-Theoretical Semantics, Outstanding Contributions to Logic 12, Springer International Publishing, pp. 499–533, 10.1007/978-3-319-62864-621.
  40. Yanjing Wang & Qinxiang Cao (2013): On axiomatizations of public announcement logic. Synthese 190(1), pp. 103–134, 10.1007/s11229-012-0233-5.

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now