
Towards Logical Specification of Statistical Machine Learning
We introduce a logical approach to formalizing statistical properties of...
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Statistical Epistemic Logic
We introduce a modal logic for describing statistical knowledge, which w...
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ESmodels: An Epistemic Specification Solver
(To appear in Theory and Practice of Logic Programming (TPLP)) ESmodel...
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Thinking About Causation: A Causal Language with Epistemic Operators
This paper proposes a formal framework for modeling the interaction of c...
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Learning Ontologies with Epistemic Reasoning: The EL Case
We investigate the problem of learning description logic ontologies from...
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Open Problems in a Logic of Gossips
Gossip protocols are programs used in a setting in which each agent hold...
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Robust Modeling of Epistemic Mental States
This work identifies and advances some research challenges in the analys...
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An Epistemic Approach to the Formal Specification of Statistical Machine Learning
We propose an epistemic approach to formalizing statistical properties of machine learning. Specifically, we introduce a formal model for supervised learning based on a Kripke model where each possible world corresponds to a possible dataset and modal operators are interpreted as transformation and testing on datasets. Then we formalize various notions of the classification performance, robustness, and fairness of statistical classifiers by using our extension of statistical epistemic logic (StatEL). In this formalization, we show relationships among properties of classifiers, and relevance between classification performance and robustness. As far as we know, this is the first work that uses epistemic models and logical formulas to express statistical properties of machine learning, and would be a starting point to develop theories of formal specification of machine learning.
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