Learning Action Models: Qualitative Approach

In dynamic epistemic logic, actions are described using action models. In this paper we introduce a framework for studying learnability of action models from observations. We present first results concerning propositional action models. First we check two basic learnability criteria: finite identifiability (conclusively inferring the appropriate action model in finite time) and identifiability in the limit (inconclusive convergence to the right action model). We show that deterministic actions are finitely identifiable, while non-deterministic actions require more learning power-they are identifiable in the limit. We then move on to a particular learning method, which proceeds via restriction of a space of events within a learning-specific action model. This way of learning closely resembles the well-known update method from dynamic epistemic logic. We introduce several different learning methods suited for finite identifiability of particular types of deterministic actions.Comment: 18 pages, accepted for LORI-V: The Fifth International Conference on Logic, Rationality and Interaction, October 28-31, 2015, National Taiwan University, Taipei, Taiwa

A Modal Logic for Supervised Learning

Formal learning theory formalizes the process of inferring a general result from examples, as in the case of inferring grammars from sentences when learning a language. In this work, we develop a general framework—the supervised learning game—to investigate the interaction between Teacher and Learner. In particular, our proposal highlights several interesting features of the agents: on the one hand, Learner may make mistakes in the learning process, and she may also ignore the potential relation between different hypotheses; on the other hand, Teacher is able to correct Learner’s mistakes, eliminate potential mistakes and point out the facts ignored by Learner. To reason about strategies in this game, we develop a modal logic of supervised learning and study its properties. Broadly, this work takes a small step towards studying the interaction between graph games, logics and formal learning theory.acceptedVersio

On the Complexity of Conclusive Update

This work is concerned with finite identifiability of languages from positive data. We focus on the characterization of finite identifiability [Mukouchi (1992), Lange and Zeugmann (1992)], which uses definite finite tell-tale sets (DFTTs for short), finite subsets of languages which are uniquely characteristic for them. We introduce preset learners, learning functions that explicitly use (collections of) DFTTs, and, in cases where there exist only finitely many DFTTs for each language, strict preset learners which in each case use this whole finite collection. We also introduce the concept of fastest learner, a learner which comes up with the right conjecture on any input string that objectively leaves only the right choice of language. We study the use of minimal DFTTs and their influence on the speed of finite identification. We show that: (a) in the case of finite collections of finite sets—finding a minimal DFTT is polynomial time computable, while finding a minimal-size DFTT is NP-complete; (b) in the general case—finite identifiability, minimal strict preset finite identifiability and fastest finite identifiability are shown to be mutually nonequivalent. In the end we mention the relevance of this work for dynamic epistemic logic