Dynamic epistemic logic with branching temporal structures
van Bentham et al. (Merging frameworks for interaction: DEL and ETL, 2007) provides a framework for generating the models of Epistemic Temporal Logic (ETL: Fagin et al., Reasoning about knowledge, 1995; Parikh and Ramanujam, Journal of Logic, Language, and Information, 2003) from the models of Dynamic Epistemic Logic (DEL: Baltag et al., in: Gilboa (ed.) Tark 1998, 1998; Gerbrandy, Bisimulations on Planet Kripke, 1999). We consider the logic TDEL on the merged semantic framework, and its extension with the labeled past-operator “P ϵ” (“The event ϵ has happened before which. . .”). To axiomatize the extension, we introduce a method for transforming a given model into a normal form in a suitable sense. These logics suggest further applications of DEL in the theory of agency, the theory of learning, etc.
KeywordsModal logic Epistemic logic DEL ETL Dynamic epistemic logic Epistemic temporal logic
Unable to display preview. Download preview PDF.
- Baltag, A., Moss, L., & Solecki, S. (1998). The logic of public announcements, common knowledge and private suspicions. In I. Gilboa (Ed.) TARK 1998 (pp. 43–56).Google Scholar
- Fagin R., Halpern J., Moses Y., Vardi M. (1995) Reasoning about knowledge. MIT Press, Synthese Library. BostonGoogle Scholar
- Gerbrandy, J. (1999). Bisimulations on Planet Kripke. PhD thesis, ILLC.Google Scholar
- Hoshi, T. (2008). Logics of public announcement with constrained protocols. LOFT.Google Scholar
- Shoham Y., Leyton-Brown K. (2008) Multiagent systems: Algorithmic, game-theoretic, and logical foundations. Cambridge University Press, CambridgeGoogle Scholar
- van Benthem, J., Gerbrandy, J., Hoshi, T., & Pacuit, E. (2007). Merging frameworks for interaction: DEL and ETL.Google Scholar
- van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic Epistemi Logic, volume 337 of Synthese Library. Springer.Google Scholar
- Yap, A. (2007). Dynamic epistemic logic and temporal modality. Dynamic Logic Montréal.Google Scholar