Constraint answer set programming or CASP, for short, is a hybrid approach in
automated reasoning putting together the advances of distinct research areas
such as answer set programming, constraint processing, and satisfiability
modulo theories. Constraint answer set programming demonstrates promising
results, including the development of a multitude of solvers: acsolver,
clingcon, ezcsp, idp, inca, dingo, mingo, aspmt, clingo[l,dl], and ezsmt. It
opens new horizons for declarative programming applications such as solving
complex train scheduling problems. Systems designed to find solutions to
constraint answer set programs can be grouped according to their construction
into, what we call, integrational or translational approaches. The focus of
this paper is an overview of the key ingredients of the design of constraint
answer set solvers drawing distinctions and parallels between integrational and
translational approaches. The paper also provides a glimpse at the kind of
programs its users develop by utilizing a CASP encoding of Travelling Salesman
problem for illustration. In addition, we place the CASP technology on the map
among its automated reasoning peers as well as discuss future possibilities for
the development of CASP.

本文提出了 Constraint answer set programming 技术的概述，重点介绍了整合法和翻译法两种设计 Constraint answer set 求解器的方法，并提供了一个基于该技术的 Traveling Salesman Problem 的编码实例。

约束答案集编程：集成与转化（或基于 SMT 的）方法

Constraint Answer Set Programming: Integrational and Translational (or  SMT-based) Approaches

Constraint answer set programming integrates answer set programming with
constraint processing. System EZSMT+ is a constraint answer set programming
tool that utilizes satisfiability modulo theory solvers for search. Its
theoretical foundation lies on generalizations of Niemela's characterization of
answer sets of a logic program via so called level rankings.

该研究使用基于满足性模理论求解器的约束应答集编程工具 EZSMT+，其理论基础是通过所谓的级别排名对逻辑程序的应答集进行推广的 Niemela 的表征。

基于 SMT 的约束答案集求解器 EZSMT+

SMT-based Constraint Answer Set Solver EZSMT+

Researchers in answer set programming and constraint programming have spent
significant efforts in the development of hybrid languages and solving
algorithms combining the strengths of these traditionally separate fields.
These efforts resulted in a new research area: constraint answer set
programming. Constraint answer set programming languages and systems proved to
be successful at providing declarative, yet efficient solutions to problems
involving hybrid reasoning tasks. One of the main contributions of this paper
is the first comprehensive account of the constraint answer set language and
solver EZCSP, a mainstream representative of this research area that has been
used in various successful applications. We also develop an extension of the
transition systems proposed by Nieuwenhuis et al. in 2006 to capture Boolean
satisfiability solvers. We use this extension to describe the EZCSP algorithm
and prove formal claims about it. The design and algorithmic details behind
EZCSP clearly demonstrate that the development of the hybrid systems of this
kind is challenging. Many questions arise when one faces various design choices
in an attempt to maximize system's benefits. One of the key decisions that a
developer of a hybrid solver makes is settling on a particular integration
schema within its implementation. Thus, another important contribution of this
paper is a thorough case study based on EZCSP, focused on the various
integration schemas that it provides.
Under consideration in Theory and Practice of Logic Programming (TPLP).

本研究提出了约束应答集编程 Constraint Answer Set Programming （CASP）新研究领域，开发相应的 EZCSP 语言及其解释器并对其进行了系统性的研究，其设计和算法细节清晰地证明了这种混合系统的发展具有挑战性。在此基础上，展开了基于 EZCSP 的案例研究，重点关注其提供的各种集成方式。

约束求解器 EZCSP 及其集成架构的重要性

Constraint Answer Set Solver EZCSP and Why Integration Schemas Matter

PDDL+ is an extension of PDDL that enables modelling planning domains with
mixed discrete-continuous dynamics. In this paper we present a new approach to
PDDL+ planning based on Constraint Answer Set Programming (CASP), i.e. ASP
rules plus numerical constraints. To the best of our knowledge, ours is the
first attempt to link PDDL+ planning and logic programming. We provide an
encoding of PDDL+ models into CASP problems. The encoding can handle non-linear
hybrid domains, and represents a solid basis for applying logic programming to
PDDL+ planning. As a case study, we consider the EZCSP CASP solver and obtain
promising results on a set of PDDL+ benchmark problems.

本文提出了一种新的基于约束应答集规划的 PDDL + 计划方法，在将 PDDL + 模型编码为 CASP 问题的基础上，处理混合离散 - 连续动力学领域，这是将 PDDL + 计划和逻辑编程联系起来的首次尝试，并以 EZCSP CASP 求解器为案例研究，在一组 PDDL + 基准问题上获得了有希望的结果。