Learning Possibilistic Logic Theories from Default Rules
This work addresses the challenge of constructing logical theories from uncertain or conflicting data, which is incremental in applying possibilistic logic to crowdsourced data and Markov logic approximations.
The paper tackles the problem of learning possibilistic logic theories from default rules, analyzing VC dimension and complexity, and presents a scalable heuristic algorithm that handles noisy and conflicting defaults, with experimental results demonstrating effectiveness.
We introduce a setting for learning possibilistic logic theories from defaults of the form "if alpha then typically beta". We first analyse this problem from the point of view of machine learning theory, determining the VC dimension of possibilistic stratifications as well as the complexity of the associated learning problems, after which we present a heuristic learning algorithm that can easily scale to thousands of defaults. An important property of our approach is that it is inherently able to handle noisy and conflicting sets of defaults. Among others, this allows us to learn possibilistic logic theories from crowdsourced data and to approximate propositional Markov logic networks using heuristic MAP solvers. We present experimental results that demonstrate the effectiveness of this approach.