Answer Set Programming (ASP) is a well-established paradigm for declarative programming and nonmonotonic reasoning. ASP allows for flexible modeling using rules. ASP rules induce a set of intended models called answer sets. Incoherence, the non-existence of answer sets, is therefore a feature of ASP, indicating that the rules admit no intended models. However, this feature can also be problematic in certain circumstances: errors that cause incoherence are notoriously difficult to debug, and query answering will not provide any meaningful answers for incoherent programs. Paracoherent semantics have been suggested as a remedy. They extend the classical notion of answer sets to draw meaningful conclusions also from incoherent programs. However, paracoherent semantics have essentially been inapplicable in practice, due to the lack of efficient algorithms and implementations. In this paper, this lack is addressed, and several different algorithms to compute semi-stable and semi-equilibrium models are proposed and implemented within an answer set solving framework. A key role in the framework is played by syntactic program transformations that allow for characterizing paracoherent semantics in terms of the answer sets of transformed programs. Apart from existing transformations from the literature, a novel transformation is also proposed, which provides an alternative characterization of paracoherent semantics in terms of (extended) externally supported models. Notably, the new transformation is more compact than the existing ones, and brings performance benefits. An extensive empirical performance comparison among the algorithms on benchmarks from ASP competitions and a real-world use case is given as well. It shows not only that the methods developed in this paper lead to practically effective systems, but also show a clear advantage of the methods that rely on (extended) externally supported models.

答案集编程（ASP）是用于声明式编程和非单调推理的公认范例。ASP允许使用规则进行灵活的建模。ASP规则产生了一组预期的模型，称为答案集。因此，不连贯性（答案集的不存在）是ASP的一项功能，表明规则不允许任何预期的模型。但是，此功能在某些情况下也可能会带来问题：众所周知，导致不连贯的错误很难调试，并且查询应答不会为不连贯的程序提供任何有意义的答案。已经提出了超相干语义作为一种补救措施。他们扩展了经典的答案集概念，也从不连贯的程序中得出了有意义的结论。但是，超相干语义在实践中基本上是不适用的，由于缺乏有效的算法和实现。在本文中，解决了这一不足，并提出了几种不同的算法来计算半稳定和半平衡模型，并在答案集求解框架内实现了该算法。语法程序转换在框架中扮演着关键角色，该程序转换允许根据转换后程序的答案集来表征超相干语义。除了文献中已有的变换之外，还提出了一种新颖的变换，该变换根据（扩展的）外部支持的模型提供了对相干语义的另一种表征。值得注意的是，新的转换比现有的转换更紧凑，并且带来了性能上的好处。还给出了基于ASP竞争基准的算法与实际使用案例之间广泛的经验性能比较。它不仅表明本文开发的方法可导致实际有效的系统，而且还显示出依赖于（扩展的）外部支持模型的方法的明显优势。