On the Right Path: 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. Although empirical evidence suggests that children can learn a language without responding to the correction of linguistic mistakes, the importance of Teacher in many other paradigms is significant. Instead of focusing only on learner(s), this work develops a general framework---the supervised learning game (SLG)---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 (SLL). Broadly, this work takes a small step towards studying the interaction between graph games, logics and formal learning theory.Comment: The paper was accepted by LORI 2019. But due to the page-limit constraints, that Proceedings version does not include any proofs. In this version, we show the proofs for the result

Epistemic justification and epistemic luck

Among epistemologists, it is not uncommon to relate various forms of epistemic luck to the vexed debate between internalists and externalists. But there are many internalism/externalism debates in epistemology, and it is not always clear how these debates relate to each other. In the present paper I investigate the relation between epistemic luck and prominent internalist and externalist accounts of epistemic justification. I argue that the dichotomy between internalist and externalist concepts of justification can be characterized in terms of epistemic luck. Whereas externalist theories of justification are incompatible with veritic luck but not with reflective luck, the converse is true for internalist theories of justification. These results are found to explain and cohere with some recent findings from elsewhere in epistemology, and support a surprising picture of justification, on which internalism and externalism are complementary rather than contradictory positions

Economic Analysis of Knowledge: The History of Thought and the Central Themes

Following the development of knowledge economies, there has been a rapid expansion of economic analysis of knowledge, both in the context of technological knowledge in particular and the decision theory in general. This paper surveys this literature by identifying the main themes and contributions and outlines the future prospects of the discipline. The wide scope of knowledge related questions in terms of applicability and alternative approaches has led to the fragmentation of research. Nevertheless, one can identify a continuing tradition which analyses various aspects of the generation, dissemination and use of knowledge in the economy

Belief-Forming Processes, Extended

We very often grant that a person can gain knowledge on the basis of epistemic artifacts such as telescopes, microscopes and so on. However, this intuition threatens to undermine virtue reliabilism according to which one knows that p if and only if one’s believing the truth that p is the product of a reliable cognitive belief-forming process; in an obvious sense epistemic artifacts are not parts of one’s overall cognitive system. This is so, unless the extended cognition hypothesis (HEC) is true. According to HEC when parts of the environment become properly coupled to the agent’s brain then they too can be considered constitutive parts of the overall cognitive mechanism—i.e. cognition potentially extends to the world surrounding the agent. Interestingly, HEC and the broader framework of virtue reliabilism share some intriguing similarities, which render these two views mutually supportive. Making these similarities explicit provides a principled account of the way in which our knowledge-conducive cognitive characters may extend beyond our natural cognitive capacities by incorporating epistemic artifacts