Knowledge compilation transforms logical theories into circuit representations that support efficient reasoning. We study this problem for propositional groundings of FO², the two-variable fragment of first-order logic over finite domains. Given an FO² sentence and a domain of size n, its grounding yields a propositional theory over ground atoms. We ask whether such theories admit compact representations in DNNF-based and related knowledge compilation languages, and whether these can be constructed efficiently, both with respect to the domain size n for a fixed sentence. We show first that compact compilation is impossible in general: there exists an FO² sentence whose grounding over a domain of size n requires DNNF size 2^Ω(n). On the positive side, we develop a two-stage compiler that exploits the symmetries inherent in the propositional groundings of FO² sentences. It branches on unary and binary types rather than individual ground atoms, in a similar spirit to lifted inferences for probabilistic relational models. Moreover, it optimizes the compilation process by efficiently identifying and caching residual subproblems that are equivalent with respect to future extensions. Experiments show the practical efficiency of our approach, which often produces smaller circuits and compiles faster than straightforward grounding-based baselines.

We study the model enumeration problem of the function-free, finite domain fragment of first-order logic with two variables (FO2). Specifically, given an FO2sentence Γ and a positive integer n, how can one enumerate all the models of Γ over a domain of size n? In this paper, we devise a novel algorithm to address this problem. The delay complexity, the time required between producing two consecutive models, of our algorithm is quadratic in the given domain size n (up to logarithmic factors) when the sentence is fixed. This complexity is almost optimal since the interpretation of binary predicates in any model requires at least Ω(n2) bits to represent.

Recent years have witnessed the rapid development of car-hailing services, which provide a convenient approach for connecting passengers and local drivers using their personal vehicles. At the same time, the concern on passenger safety has gradually emerged and attracted more and more attention. While car-hailing service providers have made considerable efforts on developing real-time trajectory tracking systems and alarm mechanisms, most of them only focus on providing rescue-supporting information rather than preventing potential crimes. Recently, the newly available large-scale car-hailing order data have provided an unparalleled chance for researchers to explore the risky travel area and behavior of car-hailing services, which can be used for building an intelligent crime early warning system. To this end, in this article, we propose a Risky Area and Risky Behavior Evaluation System (RARBEs) based on the real-world car-hailing order data. In RARBEs, we first mine massive multi-source urban data and train an effective area risk prediction model, which estimates area risk at the urban block level. Then, we propose a transverse and longitudinal double detection method, which estimates behavior risk based on two aspects, including fraud trajectory recognition and fraud patterns mining. In particular, we creatively propose a bipartite graph-based algorithm to model the implicit relationship between areas and behaviors, which collaboratively adjusts area risk and behavior risk estimation based on random walk regularization. Finally, extensive experiments on multi-source real-world urban data clearly validate the effectiveness and efficiency of our system.