逻辑程序答案集的见证

IF 0.7 4区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS ACM Transactions on Computational Logic Pub Date : 2022-10-20 DOI:10.1145/3568955
Yisong Wang, Thomas Eiter, Yuanlin Zhang, Fangzhen Lin
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引用次数: 2

摘要

在本文中,我们考虑答案集编程(ASP)。它是一种说明性的问题解决范例,可用于将问题编码为逻辑程序,其答案集对应于问题的解决方案。它已广泛应用于人工智能等各个领域。假设答案集应该产生原始问题的解决方案,那么“为什么一组原子是答案集”这个问题对于语义理解和程序调试都变得很重要。对于一般的逻辑程序,它已经得到了很好的研究。然而,对于作为普通逻辑程序的实质扩展的析取逻辑程序来说,这个问题并没有得到太多的解决。在本文中,我们提出了析取逻辑程序的约简概念,并展示了它如何为上述问题提供答案。首先,我们展示了对于每个答案集,它的约简为其中的每个原子提供了分辨率证明。然后,我们进一步考虑最小规则集,这些规则集将足以为原子集提供分辨率证明。这些规则集将被称为证人,是本文的重点。我们研究了计算各种证人的复杂性问题,并提供了计算这些证人的算法。特别地,我们证明了这个问题对于普通的和无头循环的析取逻辑程序是可处理的,而对于一般的析取逻辑程序是难以处理的。我们还进行了一些实验,发现对于许多著名的ASP和SAT基准测试,计算答案集原子的最小见证值通常是可行的。
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Witnesses for Answer Sets of Logic Programs
In this article, we consider Answer Set Programming (ASP). It is a declarative problem solving paradigm that can be used to encode a problem as a logic program whose answer sets correspond to the solutions of the problem. It has been widely applied in various domains in AI and beyond. Given that answer sets are supposed to yield solutions to the original problem, the question of “why a set of atoms is an answer set” becomes important for both semantics understanding and program debugging. It has been well investigated for normal logic programs. However, for the class of disjunctive logic programs, which is a substantial extension of that of normal logic programs, this question has not been addressed much. In this article, we propose a notion of reduct for disjunctive logic programs and show how it can provide answers to the aforementioned question. First, we show that for each answer set, its reduct provides a resolution proof for each atom in it. We then further consider minimal sets of rules that will be sufficient to provide resolution proofs for sets of atoms. Such sets of rules will be called witnesses and are the focus of this article. We study complexity issues of computing various witnesses and provide algorithms for computing them. In particular, we show that the problem is tractable for normal and headcycle-free disjunctive logic programs, but intractable for general disjunctive logic programs. We also conducted some experiments and found that for many well-known ASP and SAT benchmarks, computing a minimal witness for an atom of an answer set is often feasible.
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来源期刊
ACM Transactions on Computational Logic
ACM Transactions on Computational Logic 工程技术-计算机:理论方法
CiteScore
2.30
自引率
0.00%
发文量
37
审稿时长
>12 weeks
期刊介绍: TOCL welcomes submissions related to all aspects of logic as it pertains to topics in computer science. This area has a great tradition in computer science. Several researchers who earned the ACM Turing award have also contributed to this field, namely Edgar Codd (relational database systems), Stephen Cook (complexity of logical theories), Edsger W. Dijkstra, Robert W. Floyd, Tony Hoare, Amir Pnueli, Dana Scott, Edmond M. Clarke, Allen E. Emerson, and Joseph Sifakis (program logics, program derivation and verification, programming languages semantics), Robin Milner (interactive theorem proving, concurrency calculi, and functional programming), and John McCarthy (functional programming and logics in AI). Logic continues to play an important role in computer science and has permeated several of its areas, including artificial intelligence, computational complexity, database systems, and programming languages. The Editorial Board of this journal seeks and hopes to attract high-quality submissions in all the above-mentioned areas of computational logic so that TOCL becomes the standard reference in the field. Both theoretical and applied papers are sought. Submissions showing novel use of logic in computer science are especially welcome.
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