The use of meta-rules in logic, i.e., rules whose content includes other
rules, has recently gained attention in the setting of non-monotonic reasoning:
a first logical formalisation and efficient algorithms to compute the
(meta)-extensions of such theories were proposed in Olivieri et al (2021) This
work extends such a logical framework by considering the deontic aspect. The
resulting logic will not just be able to model policies but also tackle
well-known aspects that occur in numerous legal systems. The use of Defeasible
Logic (DL) to model meta-rules in the application area we just alluded to has
been investigated. Within this line of research, the study mentioned above was
not focusing on the general computational properties of meta-rules.
This study fills this gap with two major contributions. First, we introduce
and formalise two variants of Defeasible Deontic Logic with Meta-Rules to
represent (1) defeasible meta-theories with deontic modalities, and (2) two
different types of conflicts among rules: Simple Conflict Defeasible Deontic
Logic, and Cautious Conflict Defeasible Deontic Logic. Second, we advance
efficient algorithms to compute the extensions for both variants.

本文针对行为规范方面，将 Meta rules 适用于可撤销逻辑中，提出了两个变体的 Defeasible Deontic Logic，并针对这两个变体提出了高效的算法，此方法可适用于法规和信息技术领域。

伦理元规则

Deontic Meta-Rules

We propose an efficient interpretable neuro-symbolic model to solve Inductive
Logic Programming (ILP) problems. In this model, which is built from a set of
meta-rules organised in a hierarchical structure, first-order rules are
invented by learning embeddings to match facts and body predicates of a
meta-rule. To instantiate it, we specifically design an expressive set of
generic meta-rules, and demonstrate they generate a consequent fragment of Horn
clauses. During training, we inject a controlled \pw{Gumbel} noise to avoid
local optima and employ interpretability-regularization term to further guide
the convergence to interpretable rules. We empirically validate our model on
various tasks (ILP, visual genome, reinforcement learning) against several
state-of-the-art methods.

提出一种高效、可解释的神经符号模型来解决归纳逻辑编程问题，并通过实验验证其性能。