The recent series 5 of the ASP system clingo provides generic means to
enhance basic Answer Set Programming (ASP) with theory reasoning capabilities.
We instantiate this framework with different forms of linear constraints,
discuss the respective implementations, and present techniques of how to use
these constraints in a reactive context. More precisely, we introduce
extensions to clingo with difference and linear constraints over integers and
reals, respectively, and realize them in complementary ways. Finally, we
empirically evaluate the resulting clingo derivatives clingo[dl] and clingo[lp]
on common fragments and contrast them to related ASP systems.
This paper is under consideration for acceptance in TPLP.

该研究论文介绍了一种基于 ASP 系统 clingo 的算法框架，利用线性约束扩充基本 ASP，实现了不同形式的线性约束，并在反应式环境下演示其应用。最后，对该算法进行了实证评估。

Clingo 线性约束与整数和实数

Clingo goes Linear Constraints over Reals and Integers

We present the new ASP system clingo 4. Unlike its predecessors, being mere
monolithic combinations of the grounder gringo with the solver clasp, the new
clingo 4 series offers high-level constructs for realizing complex reasoning
processes. Among others, such processes feature advanced forms of search, as in
optimization or theory solving, or even interact with an environment, as in
robotics or query-answering. Common to them is that the problem specification
evolves during the reasoning process, either because data or constraints are
added, deleted, or replaced. In fact, clingo 4 carries out such complex
reasoning within a single integrated ASP grounding and solving process. This
avoids redundancies in relaunching grounder and solver programs and benefits
from the solver's learning capacities. clingo 4 accomplishes this by
complementing ASP's declarative input language by control capacities expressed
via the embedded scripting languages lua and python. On the declarative side,
clingo 4 offers a new directive that allows for structuring logic programs into
named and parameterizable subprograms. The grounding and integration of these
subprograms into the solving process is completely modular and fully
controllable from the procedural side, viz. the scripting languages. By
strictly separating logic and control programs, clingo 4 also abolishes the
need for dedicated systems for incremental and reactive reasoning, like iclingo
and oclingo, respectively, and its flexibility goes well beyond the advanced
yet still rigid solving processes of the latter.

介绍了新的 ASP 系统 clingo 4，其提供高级结构来实现复杂推理过程，支持高级搜索形式（如优化或理论求解），并通过嵌入脚本语言 lua 和 python 实现控制能力，为 ASP 的声明输入语言提供了一种新的指令来支持命名和可参数化子程序的逻辑程序结构化。通过严格分离逻辑程序和控制程序，clingo 4 还取消了增量和反应推理的专用系统，其灵活性超越了 iclbingo 和 oclingo 的解决过程。