The study of Description Logics have been historically mostly focused on
features that can be translated to decidable fragments of first-order logic. In
this paper, we leave this restriction behind and look for useful and decidable
extensions outside first-order logic. We introduce universally quantified
concepts, which take the form of variables that can be replaced with arbitrary
concepts, and define two semantics of this extension. A schema semantics allows
replacements of concept variables only by concepts from a particular language,
giving us axiom schemata similar to modal logics. A second-order semantics
allows replacement of concept variables with arbitrary subsets of the domain,
which is similar to quantified predicates in second-order logic.
To study the proposed semantics, we focus on the extension of the description
logic $\mathcal{EL}$. We show that for a useful fragment of the extension, the
conclusions entailed by the different semantics coincide, allowing us to use
classical $\mathcal{EL}$ reasoning algorithms even for the second-order
semantics. For a slightly smaller, but still useful, fragment, we were also
able to show polynomial decidability of the extension. This fragment, in
particular, can express a generalized form of role chain axioms, positive self
restrictions, and some forms of (local) role-value-maps from KL-ONE, without
requiring any additional constructors.

该论文涉及描述逻辑的特性，首次引入普遍量化的概念，提出两种扩展的语义模型，包括模态逻辑中的公理原型和二阶逻辑中的量词的替代。研究表明，在某些扩展的语义中，所得出的结论与经典的描述逻辑相符，并证明了某种程度上用于这种扩展的算法的多项式可判定性。

描述逻辑进入二阶：使用全量量化概念扩展 EL

Description Logics Go Second-Order -- Extending EL with Universally  Quantified Concepts

Over the past years, there has been a resurgence of Datalog-based systems in
the database community as well as in industry. In this context, it has been
recognized that to handle the complex knowl\-edge-based scenarios encountered
today, such as reasoning over large knowledge graphs, Datalog has to be
extended with features such as existential quantification. Yet, Datalog-based
reasoning in the presence of existential quantification is in general
undecidable. Many efforts have been made to define decidable fragments. Warded
Datalog+/- is a very promising one, as it captures PTIME complexity while
allowing ontological reasoning. Yet so far, no implementation of Warded
Datalog+/- was available. In this paper we present the Vadalog system, a
Datalog-based system for performing complex logic reasoning tasks, such as
those required in advanced knowledge graphs. The Vadalog system is Oxford's
contribution to the VADA research programme, a joint effort of the universities
of Oxford, Manchester and Edinburgh and around 20 industrial partners. As the
main contribution of this paper, we illustrate the first implementation of
Warded Datalog+/-, a high-performance Datalog+/- system utilizing an aggressive
termination control strategy. We also provide a comprehensive experimental
evaluation.

本文介绍了 Vadalog 系统，这是使用 Datalog 进行复杂逻辑推论任务的系统，采用侵略性终止控制策略实现了 Warded Datalog+/-，并提供了全面的实验评估。