Inconsistent political statements represent a form of misinformation. They erode public trust and pose challenges to accountability, when left unnoticed. Detecting inconsistencies automatically could support journalists in asking clarification questions, thereby helping to keep politicians accountable. We propose the Inconsistency detection task and develop a scale of inconsistency types to prompt NLP-research in this direction. To provide a resource for detecting inconsistencies in a political domain, we present a dataset of 698 human-annotated pairs of political statements with explanations of the annotators' reasoning for 237 samples. The statements mainly come from voting assistant platforms such as Wahl-O-Mat in Germany and Smartvote in Switzerland, reflecting real-world political issues. We benchmark Large Language Models (LLMs) on our dataset and show that in general, they are as good as humans at detecting inconsistencies, and might be even better than individual humans at predicting the crowd-annotated ground-truth. However, when it comes to identifying fine-grained inconsistency types, none of the model have reached the upper bound of performance (due to natural labeling variation), thus leaving room for improvement. We make our dataset and code publicly available.

The Honor Magic 6 Pro is a strange phone. It folds innovative new AI features, secure 3D face unlock, cutting-edge battery tech, and a powerful camera into an expensively sleek body. But the MagicOS software is buggy, the camera is inconsistent, and it's one of the most expensive Android phones on the market. While the Honor Magic 6 Pro has delighted and impressed me over the past couple of weeks, it has also frustrated and confused me. It can be oh-so-slick one minute and trip up the next.

Among the local consistency techniques used for solving constraint networks, path-consistency (PC) has received a great deal of attention. However, enforcing PC is computationally expensive and sometimes even unnecessary. Directional path-consistency (DPC) is a weaker notion of PC that considers a given variable ordering and can thus be enforced more efficiently than PC. This paper shows that DPC (the DPC enforcing algorithm of Dechter and Pearl) decides the constraint satisfaction problem (CSP) of a constraint language if it is complete and has the variable elimination property (VEP). However, we also show that no complete VEP constraint language can have a domain with more than 2 values. We then present a simple variant of the DPC algorithm, called DPC*, and show that the CSP of a constraint language can be decided by DPC* if it is closed under a majority operation. In fact, DPC* is sufficient for guaranteeing backtrack-free search for such constraint networks. Examples of majority-closed constraint classes include the classes of connected row-convex (CRC) constraints and tree-preserving constraints, which have found applications in various domains, such as scene labeling, temporal reasoning, geometric reasoning, and logical filtering. Our experimental evaluations show that DPC* significantly outperforms the state-of-the-art algorithms for solving majority-closed constraints.