Learning Possibilistic Logic Theories from Default Rules

TL;DR

This paper presents a scalable method for learning possibilistic logic theories from default rules, capable of handling noise and conflicts, with applications to crowdsourced data and Markov logic networks.

Contribution

It introduces a new learning framework for possibilistic logic from defaults, analyzes its theoretical properties, and provides a heuristic algorithm with practical scalability.

Findings

The VC dimension of possibilistic stratifications is characterized.

The heuristic learning algorithm scales to thousands of defaults.

Experimental results show the approach's effectiveness in real-world scenarios.

Abstract

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.