Bridging learning theory and dynamic epistemic logic

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

Description logic · Doxastic logic · Dynamic logic (digital electronics) · Epistemic modal logic · Epistemology · Inference · Iterated function · Metaphysics · Modal · Modal logic · Multimodal logic · Philosophy of language · Philosophy of logic · Philosophy of science · Artificial Intelligence · Computer Science · Logic, programming, and type systems · Logic, Reasoning, and Knowledge · Machine Learning and Algorithms · Mathematics · Philosophy

• Dynamic Epistemic Logic

  Open Access•Hans van Ditmarsch, Wiebe Van Der Hoek et al.•Dynamic Epistemic Logic•2008

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• The Logic of Reliable Inquiry

  Kevin T Kelly•The logic of reliable inquiry•1996

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• Language identification in the limit

  Open Access•E Mark Gold, Eric Gold•Information and Control•1967

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• Knowledge and Belief

  Open Access•P T Geach•Philosophical Books•1963

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• Logics for Epistemic Programs

  Open Access•Alexandru Baltag, Lawrence S Mo et al.•Synthese•2004

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