Learning in a Changing World, an Algebraic Modal Logical Approach
We develop an algebraic modal logic that combines epistemic and dynamic modalities with a view to modelling information acquisition (learning) by automated agents in a changing world. Unlike most treatments of dynamic epistemic logic, we have transitions that “change the state” of the underlying system and not just the state of knowledge of the agents. The key novel feature that emerges is the need to have a way of “inverting transitions” and distinguishing between transitions that “really happen” and transitions that are possible.
Our approach is algebraic, rather than being based on a Kripke-style semantics. The semantics are given in terms of quantales. We study a class of quantales with the appropriate inverse operations and prove properties of the setting. We illustrate the ideas with toy robot-navigation problems. These illustrate how an agent learns information by taking actions.
KeywordsReal Action Robot Navigation Epistemic Logic Epistemic Modality Kripke Structure
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- [vanDit05]van Ditmarsch, H.P., van der Hoek, W., Kooi, B.P.: Dynamic Epistemic Logic with Assignment. In: Proceedings of AAMAS, pp. 141–148 (2005)Google Scholar
- [HM84]Halpern, J.Y., Moses, Y.: Knowledge and common knowledge in a distributed environment. In: Proceedings of the Third ACM Symposium on Principles of Distributed Computing, pp. 50–61 (1984); A revised version appears as IBM Research Report RJ 4421 (August 1987)Google Scholar
- [PS10]Panangaden, P., Sadrzadeh, M.: Learning in a changing world via algebraic modal logic, http://www.comlab.ox.ac.uk/files/2815/mehrnoosh_prakash.pdf and http://www.cs.mcgill.ca/~prakash/Pubs/mehrnoosh_prakash.pdf
- [Phi09]Phillips, C.: An algebraic approach to dynamic epistemic logic. Master’s thesis, School of Computer Sciecne. McGill University (2009)Google Scholar
- [Sad06]Sadrzadeh, M.: Actions and Resources in Epistemic Logic. PhD thesis, Université du Québec à Montréal (2006)Google Scholar