Induction of Interpretable Possibilistic Logic Theories from Relational Data

Abstract

The field of Statistical Relational Learning (SRL) is concerned with learning probabilistic models from relational data. Learned SRL models are typically represented using some kind of weighted logical formulas, which make them considerably more interpretable than those obtained by e.g. neural networks. In practice, however, these models are often still difficult to interpret correctly, as they can contain many formulas that interact in non-trivial ways and weights do not always have an intuitive meaning. To address this, we propose a new SRL method which uses possibilistic logic to encode relational models. Learned models are then essentially stratified classical theories, which explicitly encode what can be derived with a given level of certainty. Compared to Markov Logic Networks (MLNs), our method is faster and produces considerably more interpretable models.

Possibility Theory and Possibilistic Logic: Tools for Reasoning Under and About Incomplete Information

“…Indeed having a stratified set of first-order logic rules as an hypothesis in ILP is of interest for learning both rules covering normal cases and more specific rules for exceptional cases [62]. A different approach to the induction of possibilistic logic theories is proposed in [51]. It relies on the fact that any set of formulas in Markov logic [61] can be exactly translated into possibilistic logic formulas [50,46].…”

VC-Dimension Based Generalization Bounds for Relational Learning

“…Relational examples The learning setting considered in this paper follows the one that was introduced in [9,8]. The central notion is that of a relational example (or simply example if there is no cause for confusion),which is defined as a pair (A, C), with C a set of constants and A a set of ground atoms which only use constants from C. A relational example is intended to provide a complete description of a possible world, hence any ground atom over C which is not contained in A is implicitly assumed to be false.…”

“…Clearly, in order to provide any guarantees on the accuracy of these predictions, we need to make (simplifying) assumptions about how the training structures are obtained. In this paper, we follow the setting from [9,8], where it is assumed that these structures are all obtained as fragments induced by domain elements sampled uniformly without replacement.…”

“…The specific problem that we consider in this paper is to bound the error that we make when estimating probabilities of first-order theories from the training example, or more specifically, the probability that a first-order theory Φ is satisfied in a small randomly sampled fragment of the relational structure. While this setting has already been studied in [9,8,7], one important remaining problem, which will be the focus of this paper, relates to how the theory Φ is obtained. Typically, Φ is chosen from some hypothesis class, based on the same training example that is used to estimate its probability.…”

Relational Marginal Problems: Theory and Estimation

“…Thus, first, we describe two different types of relational marginals, which differ in the kinds of statistics that are provided. 1 The first type is based on relational marginal distributions (Kuželka, Davis, and Schockaert 2017) and the second is based on Halpern-style random substitution semantics (Bacchus et al 1992). Second, for both types of statistics, we establish a relational counterpart of the duality between maximum-likelihood estimation and max-entropy marginal problems.…”