In this paper, we consider an approach introduced in term rewriting for the automatic detection of non-looping non-termination from patterns of rules. We adapt it to logic programing by defining a new unfolding technique that produces patterns describing possibly infinite sets of finite rewrite sequences. We present an experimental evaluation of our contributions that we implemented in our tool NTI (Non-Termination Inference).

Constraint Programming developed within Logic Programming in the Eighties; nowadays all Prolog systems encompass modules capable of handling constraint programming on finite domains demanding their solution to a constraint solver. This work focuses on a specific form of constraint, the so-called table constraint, used to specify conditions on the values of variables as an enumeration of alternative options. Since every condition on a set of finite domain variables can be ultimately expressed as a finite set of cases, Table can, in principle, simulate any other constraint. These characteristics make Table one of the most studied constraints ever, leading to a series of increasingly efficient propagation algorithms. Despite this, it is not uncommon to encounter real-world problems with hundreds or thousands of valid cases that are simply too many to be handled effectively with standard CPU-based approaches. In this paper, we deal with the Compact-Table (CT) algorithm, the state-of-the-art propagation algorithms for Table. We describe how CT can be enhanced by exploiting the massive computational power offered by modern Graphics Processing Units (GPUs) to handle large Table constraints. In particular, we report on the design and implementation of GPU-accelerated CT, on its integration into an existing constraint solver, and on an experimental validation performed on a significant set of instances.

Abductive reasoning is a popular non-monotonic paradigm that aims to explain observed symptoms and manifestations. It has many applications, such as diagnosis and planning in artificial intelligence and database updates. In propositional abduction, we focus on specifying knowledge by a propositional formula. The computational complexity of tasks in propositional abduction has been systematically characterized – even with detailed classifications for Boolean fragments. Unsurprisingly, the most insightful reasoning problems (counting and enumeration) are computationally highly challenging. Therefore, we consider reasoning between decisions and counting, allowing us to understand explanations better while maintaining favorable complexity. We introduce facets to propositional abductions, which are literals that occur in some explanation (relevant) but not all explanations (dispensable). Reasoning with facets provides a more fine-grained understanding of variability in explanations (heterogeneous). In addition, we consider the distance between two explanations, enabling a better understanding of heterogeneity/homogeneity. We comprehensively analyze facets of propositional abduction in various settings, including an almost complete characterization in Post’s framework.

In the context of urban traffic control, traffic signal optimisation is the problem of determining the optimal green length for each signal in a set of traffic signals. The literature has effectively tackled such a problem, mostly with automated planning techniques leveraging the PDDL + language and solvers. However, such language has limitations when it comes to specifying optimisation statements and computing optimal plans. In this paper, we provide an alternative solution to the traffic signal optimisation problem based on Constraint Answer Set Programming (CASP). We devise an encoding in a CASP language, which is then solved by means of clingcon 3, a system extending the well-known ASP solver clingo. We performed experiments on real historical data from the town of Huddersfield in the UK, comparing our approach to the PDDL+ model that obtained the best results for the considered benchmark. The results showed the potential of our approach for tackling the traffic signal optimisation problem and improving the solution quality of the PDDL + plans.

While the existence of a stable matching for the stable roommates problem possibly with incomplete preference lists (SRI) can be decided in polynomial time, SRI problems with some fairness criteria are intractable. Egalitarian SRI that tries to maximize the total satisfaction of agents if a stable matching exists, is such a hard variant of SRI. For experimental evaluations of methods to solve these hard variants of SRI, several well-known algorithms have been used to randomly generate benchmark instances. However, these benchmark instances are not always satisfiable and usually have a small number of stable matchings if one exists. For such SRI instances, despite the NP-hardness of Egalitarian SRI, it is practical to find an egalitarian stable matching by enumerating all stable matchings. In this study, we introduce a novel algorithm to generate benchmark instances for SRI that have very large numbers of solutions, and for which it is hard to find an egalitarian stable matching by enumerating all stable matchings.