Abstract
This paper discusses the possibility of modelling inductive inference (Gold 1967) in dynamic epistemic logic (see e.g. van Ditmarsch et al. 2007). The general purpose is to propose a semantic basis for designing a modal logic for learning in the limit. First, we analyze a variety of epistemological notions involved in identification in the limit and match it with traditional epistemic and doxastic logic approaches. Then, we provide a comparison of learning by erasing (Lange et al. 1996) and iterated epistemic update (Baltag and Moss 2004) as analyzed in dynamic epistemic logic. We show that finite identification can be modelled in dynamic epistemic logic, and that the elimination process of learning by erasing can be seen as iterated belief-revision modelled in dynamic doxastic logic. Finally, we propose viewing hypothesis spaces as temporal frames and discuss possible advantages of that perspective.
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References
Alchourrón C.E., Gärdenfors P., Makinson D. (1985) On the logic of theory change: Partial meet contraction and revision functions. The Journal of Symbolic Logic 50(2): 510–530
Angluin D. (1980) Inductive inference of formal languages from positive data. Information and Control 45(2): 117–135
Baltag A., Moss L. (2004) Logics for epistemic programs. Synthese 139(2): 165–224
Batlag, A., Moss, L. S., & Solecki, S. (1998). The logic of public announcements and common knowledge and private suspicions. In Proceedings of the 7th TARK (pp. 43–56).
Costa Florêntio, C. (2002). Learning generalized quantifiers. In Proceedings of the 7th ESSLLI Student Session.
Dégremont, C., & Gierasimczuk, N. (2009). Can doxastic agents learn? On the temporal structure of learning. ILLC Prepublication (PP) Series PP-2009-14, Amsterdam.
Freivalds, R., & Zeugmann, T. (1995). Co-learning of recursive languages from positive data, RIFIS. Technical report, RIFIS-TR-CS-110, RIFIS, Kyushu University 33.
Gierasimczuk, N. (2007). The problem of learning the semantics of quantifiers. In Proceedings of the 6th TbiLLC, Vol. 4363 of LNAI (pp. 117–126). Springer.
Gierasimczuk, N. (2009). Identification through inductive verification. In Proceedings of the 7th TbiLLC, Vol. 5422 of LNAI (pp. 193–205). Springer.
Gierasimczuk, N., Kurzen, L., & Velázquez-Quesada, F. (2009). Learning as interaction (manuscript).
Gold E. (1967) Language identification in the limit. Information and Control 10: 447–474
Hintikka J. (1962) Knowledge and belief. An introduction to the logic of the two notions. Cornell University Press, Ithaca
Jain S., Osherson D., Royer J.S., Sharma A. (1999) Systems that learn. MIT Press, Chicago
Kelly K. (1996) The logic of reliable inquiry. Oxford University Press, Oxford
Lange, S., Wiehagen, R., & Zeugmann, T. (1996). Learning by erasing. In Proceedings of the 7th international workshop on algorithmic learning theory (pp. 228–241). Springer-Verlag.
Martin E., Osherson D. (1998) Elements of scientific inquiry. MIT Press, Cambridge
Osherson D., de Jongh D., Martin E., Weinstein S. (1997) Formal learning theory. In: van Benthem J., Ter Meulen A. (eds) Handbook of logic and language. North Holland, Amsterdam
Tiede H.-J. (1999) Identifiability in the limit of context-free generalized quantifiers. Journal of Language and Computation 1: 93–102
van Benthem J. (1986) Essays in logical semantics. D. Reidel, Dordrecht
van Benthem, J., Gerbrandy, J., & Pacuit, E. (2007). Merging frameworks for interaction: DEL and ETL. In Proceedings of the 11th TARK (pp. 72–81).
van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic epistemic logic. Springer Netherlands.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Gierasimczuk, N. Bridging learning theory and dynamic epistemic logic. Synthese 169, 371–384 (2009). https://doi.org/10.1007/s11229-009-9549-1
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DOI: https://doi.org/10.1007/s11229-009-9549-1