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2020 | OriginalPaper | Buchkapitel

The Logic of AGM Learning from Partial Observations

verfasst von : Alexandru Baltag, Aybüke Özgün, Ana Lucia Vargas-Sandoval

Erschienen in: Dynamic Logic. New Trends and Applications

Verlag: Springer International Publishing

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Abstract

We present a dynamic logic for inductive learning from partial observations by a “rational” learner, that obeys AGM postulates for belief revision. We apply our logic to an example, showing how various concrete properties can be learnt with certainty or inductively by such an AGM learner. We present a sound and complete axiomatization, based on a combination of relational and neighbourhood version of the canonical model method.

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Vorheriges Kapitel Behavioural and Abstractor Specifications for a Dynamic Logic with Binders and Silent Transitions

Nächstes Kapitel A Dynamic Epistemic Logic Analysis of the Equality Negation Task

Indeed, our observational events can be seen as corresponding to a special type of (single-agent) epistemic events in the so-called BMS style.

A total preorder \(\le \) on X is a reflexive and transitive binary relation such that every two points are comparable: for all \(x, y\in X\), either \(x\le y\) or \(y\le x\) (or both).

Since \(\le \) is a total preorder, this definition coincides with the standard definition of maximal elements as \(Max_\le (O):=\{x\in O : \forall y\in O(x\le y \text{ implies } x\le y)\}\).

This is a standard method in Dynamic Epistemic Logic and we refer the reader to [18, Chap. 7.4] for further details.

When we quantify over learners, learnability with certainty (by some learners) matches the standard concept of “finite identifiability” from Formal Learning Theory.

When we quantify over learners, inductive learnability (by some learners) matches the standard concept of “identifiability in the limit” from Formal Learning Theory, see e.g. [13].

We use \(\preceq \) to denote the plausibility order in this frame, to distinguish it from the natural order on \(X\subseteq R\).

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Baltag, A., Gierasimczuk, N., Smets, S.: Belief revision as a truth-tracking process. In: Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge, pp. 187–190. ACM (2011)

Baltag, A., Gierasimczuk, N., Smets, S.: On the solvability of inductive problems: a study in epistemic topology. In: Ramanujam, R. (ed.) Proceedings of the 15th Conference TARK, also Available as a Technical Report in ILLC Prepublication Series PP-2015-13 (2015)

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Titel: The Logic of AGM Learning from Partial Observations
verfasst von: Alexandru Baltag
Aybüke Özgün
Ana Lucia Vargas-Sandoval
Verlag: Springer International Publishing
Buch: Dynamic Logic. New Trends and Applications
Print ISBN: 978-3-030-38807-2

Electronic ISBN: 978-3-030-38808-9

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-38808-9_3

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