Abstract. We define logic programs with defaults and argumentation theories, a new framework that unifies most of the earlier proposals for defeasible reasoning in logic programming. We present a model-theoretic semantics and study its reducibility and well-behavior properties. We use the framework as an elegant and flexible foundation to extend and improve upon Generalized Courteous Logic Programs (GCLP) [19]-one of the popular forms of defeasible reasoning. The extensions include higherorder and object-oriented features of Hilog and F-Logic [7,21]. The improvements include much simpler, incremental reasoning algorithms and more intuitive behavior. The framework and its Courteous family instantiation were implemented as an extension to the FLORA-2 system.

The Semantic Web initiative has led to an upsurge of the interest in rules as a general and powerful way of processing, combining, and analyzing semantic information. Since several of the technologies underlying rule-based systems are already quite mature, it is important to understand how such systems might perform on the Web scale. OpenRuleBench is a suite of benchmarks for analyzing the performance and scalability of different rule engines. Currently the study spans five different technologies and eleven systems, butOpenRuleBench is an open community resource, and contributions from the community are welcome. In this paper, we describe the tested systems and technologies, the methodology used in testing, and analyze the results.

A large body of work has been dedicated to termination analysis of logic programs but relatively little has been done to analyze non-termination. In our opinion, explaining non-termination is a much more important task because it can dramatically improve a user's ability to effectively debug large, complex logic programs without having to abide by punishing syntactic restrictions. Non-termination analysis examines program execution history when the program is suspected to not terminate and informs the programmer about the exact reasons for this behavior. In Liang and Kifer (2013), we studied the problem of non-termination in tabled logic engines with subgoal abstraction, such as XSB, and proposed a suite of algorithms for non-termination analysis, called Terminyzer. These algorithms analyze forest logging traces and output sequences of tabled subgoal calls that are the likely causes of non-terminating cycles. However, this feedback was hard to use in practice: the same subgoal could occur in multiple rule heads and in even more places in rule bodies, so Terminyzer left too much tedious, sometimes combinatorially large amount of work for the user to do manually.Here we propose a new suite of algorithms, Terminyzer+, which closes this usability gap. Terminyzer+ can detect not only sequences of subgoals that cause non-termination, but, importantly, the exact rules where they occur and the rule sequences that get fired in a cyclic manner, thus causing non-termination. This makes Terminyzer+ suitable as a back-end for user-friendly graphical interfaces on top of Terminyzer+, which can greatly simplify the debugging process. Terminyzer+ back-ends exist for the SILK system as well as for the open-source ${\cal F}$lora-2 system. A graphical interface has been developed for SILK and is currently underway for ${\cal F}$lora-2. We also report experimental studies, which confirm the effectiveness of Terminyzer+ on a host of large real-world knowledge bases. All tests used in this paper are available online.1In addition, we make a step towards automatic remediation of non-terminating programs by proposing an algorithm that heuristically fixes some causes of misbehavior. Furthermore, unlike Terminyzer, Terminyzer+ does not require the underlying logic engine to support subgoal abstraction, although it can make use of it.