Encoding Markov Logic Networks in Possibilistic Logic
This addresses the problem of making MLNs more interpretable for users in AI and knowledge representation, though it is incremental as it builds on existing MAP inference techniques.
The paper tackled the interpretability issue of Markov logic networks (MLNs) by proposing a method to encode them into possibilistic logic theories that capture maximum a posteriori (MAP) inference, but noted that the exact theory can be exponentially large, so they also developed compact methods for specific evidence types.
Markov logic uses weighted formulas to compactly encode a probability distribution over possible worlds. Despite the use of logical formulas, Markov logic networks (MLNs) can be difficult to interpret, due to the often counter-intuitive meaning of their weights. To address this issue, we propose a method to construct a possibilistic logic theory that exactly captures what can be derived from a given MLN using maximum a posteriori (MAP) inference. Unfortunately, the size of this theory is exponential in general. We therefore also propose two methods which can derive compact theories that still capture MAP inference, but only for specific types of evidence. These theories can be used, among others, to make explicit the hidden assumptions underlying an MLN or to explain the predictions it makes.