Statistical Relational Learning (SRL) integrates First-Order Logic (FOL) and probability theory for learning and inference over relational data. Probabilistic inference and learning in many SRL models can be reduced to Weighted First Order Model Counting (WFOMC). However, WFOMC is known to be intractable ($\mathrm{\#P_1-}$ complete). Hence, logical fragments that admit polynomial time WFOMC are of significant interest. Such fragments are called domain liftable. Recent line of works have shown the two-variable fragment of FOL, extended with counting quantifiers ($\mathrm{C^2}$) to be domain-liftable. However, many properties of real-world data can not be modelled in $\mathrm{C^2}$. In fact many ubiquitous properties of real-world data are inexressible in FOL. Acyclicity is one such property, found in citation networks, genealogy data, temporal data e.t.c. In this paper we aim to address this problem by investigating the domain liftability of directed acyclicity constraints. We show that the fragment $\mathrm{C^2}$ with a Directed Acyclic Graph (DAG) axiom, i.e., a predicate in the language is axiomatized to represent a DAG, is domain-liftable. We present a method based on principle of inclusion-exclusion for WFOMC of $\mathrm{C^2}$ formulas extended with DAG axioms.
Solving Combinatorial Counting Problems with Weighted First-Order Model Counting
School of Artificial Intelligence, Jilin University, Changchun, China；State Key Laboratory of Complex \& Critical Software Environment, Beihang University, China；National Research Center for Educational Materials, China；Tengen Intelligence Institute, China；Czech Technical University in Prague, Prague, Czech Republic
Counting and Sampling from Markov Equivalent DAGs Using Clique Trees
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Sharif University of Technology（谢里夫理工大学）；Georgia Institute of Technology（佐治亚理工学院）；Carnegie Mellon University（卡内基梅隆大学）
Causal structure learning with momentum: Sampling distributions over Markov Equivalence Classes of DAGs
Chalmers University of Technology（查尔姆斯理工大学）；University of Gothenburg（哥德堡大学）；Institute for Theoretical Computer Science（理论计算机科学研究所）；University of Lübeck（吕贝克大学）
Faster Lifting for Ordered Domains with Predecessor Relations
School of Artificial Intelligence, Jilin University, China（人工智能学院，吉林大学，中国）；College of Computer Science and Technology, Jilin University, China（计算机科学与技术学院，吉林大学，中国）；Engineering Research Center of Knowledge-Driven Human-Machine Intelligence, MOE, China（知识驱动人机智能工程研究中心，教育部，中国）；CRRC Zhuzhou Institute, Zhuzhou, China（CRRC 长沙院，长沙，中国）；Czech Technical University, Czechia（捷克技术大学，捷克）
针对有序域中前驱关系导致 WFOMC 实用性能不佳的问题，提出原生支持前驱关系的新提升推理算法，可处理一般第 k 阶前驱并取得指数级与一个数量级加速。
