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Logic and Learning

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Johan van Benthem on Logic and Information Dynamics

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 5))

Abstract

Learning and learnability have been long standing topics of interests within the linguistic, computational, and epistemological accounts of inductive inference. Johan van Benthem’s vision of the “dynamic turn” has not only brought renewed life to research agendas in logic as the study of information processing, but likewise helped bring logic and learning in close proximity. This proximity relation is examined with respect to learning and belief revision, updating and efficiency, and with respect to how learnability fits in the greater scheme of dynamic epistemic logic and scientific method.

The research of Nina Gierasimczuk is funded by an Innovational Research Incentives Scheme Veni grant 275-20-043, The Netherlands Organisation for Scientific Research (NWO).

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Notes

  1. 1.

    The terms “identifiability”, “learnability”, and “solvability” are often used interchangeably in formal learning theory. Preferring one over the others is usually determined by the wider, often philosophical, methodological, or technical context. “Identifiability” is used in technical contexts, concerned with choosing (identifying) one among many possibilities (e.g., Turing machines or grammars). “Learnability” is a broader quasi-psychological notion often assumed to be (accurately) modelled by identifiability. Finally, “solvability” occurs in more logic-oriented works, and denotes the possibility of deciding on an issue, e.g., whether a hypothesis is true or false. Obviously, the latter can also be viewed as a kind of identifiability.

  2. 2.

    In general some of the proofs require a construction of an appropriate prior plausibility order. For this some classical learning-theoretic concepts and results are used, i.e., locking sequences introduced by Blum and Blum [13], as well as finite tell-tale sets and the simple non-computable version of Angluin’s theorem [2], see also the next section.

  3. 3.

    We will use the name “conclusive learnability” interchangeably with “finite identifiability” which is also sometimes referred to as “identification with certainty”.

  4. 4.

    This section overviews the approach given in [17, 22].

  5. 5.

    The characterisation involving designated propositional letters can be replaced with one that uses nominals as markers of bottom nodes. For such an approach see Dégremont and Gierasimczuk [16].

  6. 6.

    For more complex actions performed on plausibility models in the context of the comparison between dynamic doxastic and doxastic temporal logic see van Benthem and Dégremont [11].

  7. 7.

    Hintikka took, from the very beginning, the axioms of epistemic logic to describe a strong kind of agent rationality.

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Author information

Authors and Affiliations

  1. Institute for Logic, Language and Computation, University of Amsterdam, Science Park 107, 1098 XG, Amsterdam, The Netherlands

    Nina Gierasimczuk

  2. Institute for Logic, Language and Computation, University of Amsterdam, Science Park 107, 1098 XG, Amsterdam, The Netherlands

    Dick de Jongh

  3. Department of Media, Cognition and Communication, University of Copenhagen, Njalsgade 80, 2300, Copenhagen S, Denmark

    Vincent F. Hendricks

Authors
  1. Nina Gierasimczuk
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  2. Vincent F. Hendricks
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  3. Dick de Jongh
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Corresponding author

Correspondence to Nina Gierasimczuk .

Editor information

Editors and Affiliations

  1. University of Amsterdam Inst Logic,Language & Computation, Amsterdam, The Netherlands

    Alexandru Baltag

  2. Amsterdam, The Netherlands

    Sonja Smets

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Gierasimczuk, N., Hendricks, V.F., de Jongh, D. (2014). Logic and Learning. In: Baltag, A., Smets, S. (eds) Johan van Benthem on Logic and Information Dynamics. Outstanding Contributions to Logic, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-06025-5_10

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