In recent years, there has been an increasing interest in exploiting
logically specified background knowledge in order to obtain neural models (i)
with a better performance, (ii) able to learn from less data, and/or (iii)
guaranteed to be compliant with the background knowledge itself, e.g., for
safety-critical applications. In this survey, we retrace such works and
categorize them based on (i) the logical language that they use to express the
background knowledge and (ii) the goals that they achieve.

本文综述了利用逻辑指定的背景知识以获取性能更好、学习数据更少或保证符合背景知识的神经模型的研究，并根据表达背景知识的逻辑语言和实现目标进行分类。

逻辑约束下的深度学习

Deep Learning with Logical Constraints

There has recently been an increasing interest in declarative data analysis,
where analytic tasks are specified using a logical language, and their
implementation and optimisation are delegated to a general-purpose query
engine. Existing declarative languages for data analysis can be formalised as
variants of logic programming equipped with arithmetic function symbols and/or
aggregation, and are typically undecidable. In prior work, the language of
$\mathit{limit\ programs}$ was proposed, which is sufficiently powerful to
capture many analysis tasks and has decidable entailment problem. Rules in this
language, however, do not allow for negation. In this paper, we study an
extension of limit programs with stratified negation-as-failure. We show that
the additional expressive power makes reasoning computationally more demanding,
and provide tight data complexity bounds. We also identify a fragment with
tractable data complexity and sufficient expressivity to capture many relevant
tasks.

研究了带有分层否定的限制程序的扩展，发现它的附加表达能力使推理的计算需求更高，并提供了严格的数据复杂度界限。同时识别出一个具有可操作数据复杂度和足够表达能力以捕捉许多相关任务的片段。

限制 Datalog 程序中的分层否定

Stratified Negation in Limit Datalog Programs

This papers develops a logical language for representing probabilistic causal
laws. Our interest in such a language is twofold. First, it can be motivated as
a fundamental study of the representation of causal knowledge. Causality has an
inherent dynamic aspect, which has been studied at the semantical level by
Shafer in his framework of probability trees. In such a dynamic context, where
the evolution of a domain over time is considered, the idea of a causal law as
something which guides this evolution is quite natural. In our formalization, a
set of probabilistic causal laws can be used to represent a class of
probability trees in a concise, flexible and modular way. In this way, our work
extends Shafer's by offering a convenient logical representation for his
semantical objects.
Second, this language also has relevance for the area of probabilistic logic
programming. In particular, we prove that the formal semantics of a theory in
our language can be equivalently defined as a probability distribution over the
well-founded models of certain logic programs, rendering it formally quite
similar to existing languages such as ICL or PRISM. Because we can motivate and
explain our language in a completely self-contained way as a representation of
probabilistic causal laws, this provides a new way of explaining the intuitions
behind such probabilistic logic programs: we can say precisely which knowledge
such a program expresses, in terms that are equally understandable by a
non-logician. Moreover, we also obtain an additional piece of knowledge
representation methodology for probabilistic logic programs, by showing how
they can express probabilistic causal laws.

本文介绍了一种逻辑语言，用于表示概率因果律，该语言可以被用于概率逻辑编程，并且可以自我解释为概率因果律的表示方法，从而提供了解释这些编程背后想法的新方法。