Complex Markov Logic Networks: Expressivity and Liftability

Expressivity of Planning with Horn Description Logic Ontologies (Technical Report)

State constraints in AI Planning globally restrict the legal environment states. Standard planning languages make closed-domain and closed-world assumptions. Here we address open-world state constraints formalized by planning over a description logic (DL) ontology. Previously, this combination of DL and planning has been investigated for the light-weight DL DL-Lite. Here we propose a novel compilation scheme into standard PDDL with derived predicates, which applies to more expressive DLs and is based on the rewritability of DL queries into Datalog with stratified negation. We also provide a ne…

Some logics of belief and disbelief

The introduction of explicit notions of rejection, or disbelief, into logics for knowledge representation can be justified in a number of ways. Motivations range from the need for versions of negation weaker than classical negation, to the explicit recording of classic belief contraction operations in the area of belief change, and the additional levels of expressivity obtained from an extended version of belief change which includes disbelief contraction. In this paper we present four logics of disbelief which address some or all of these intuitions. Soundness and completeness results are sup…

一阶逻辑二变量片段中的精确采样

On Exact Sampling in the Two-Variable Fragment of First-Order Logic

本文证明一阶逻辑二变量片段（FO²）在采样下具有域可提升性，即存在多项式时间采样算法，并扩展至计数约束情形，方法构造性，可应用于组合结构均匀生成及统计关系模型采样。

图神经网络的逻辑蒸馏

Logical Distillation of Graph Neural Networks

提出基于C2逻辑扩展的决策树模型，从GNN中蒸馏可解释分类器，在多种架构上达到相近准确率，且在C2可表达的真实标签下优于GNN。

超越一阶逻辑的提升推理

Lifted Inference beyond First-Order Logic

本研究扩展了C^2逻辑片段的域可提升性，使其能处理有向无环图、连通图、树和森林等现实数据属性，并提出“通过分裂计数”的新方法论，为概率推理和组合结构计数提供通用框架。

Weighted Model Counting in the two variable fragment with Cardinality Constraints: A Closed Form Formula

Weighted First-Order Model Counting (WFOMC) computes the weighted sum of the models of a first-order theory on a given finite domain. WFOMC has emerged as a fundamental tool for probabilistic inference. Algorithms for WFOMC that run in polynomial time w.r.t. the domain size are called lifted inference algorithms. Such algorithms have been developed for multiple extensions of FO2(the fragment of first-order logic with two variables) for the special case of symmetric weight functions. We introduce the concept of lifted interpretations as a tool for formulating polynomials for WFOMC. Using lifted…

Notes on neighborhood semantics for logics of unknown truths and false beliefs

In this article, we study logics of unknown truths and false beliefs under neighborhood semantics. We compare the relative expressivity of the two logics. It turns out that they are incomparable over various classes of neighborhood models, and the combination of the two logics are equally expressive as standard modal logic over any class of neighborhood models. We propose morphisms for each logic, which can help us explore the frame definability problem, show a general soundness and completeness result, and generalize some results in the literature. We axiomatize the two logics over various cl…

门级布尔进化几何注意力神经网络

Gate-level boolean evolutionary geometric attention neural networks

本文提出一种基于布尔域的门级进化几何注意力神经网络，通过布尔反应-扩散机制实现图像处理，结合自注意力与RoPE技术，具备高效率和可解释性。

推动可处理多视角推理的边界：面向 Standpoint EL+ 的演绎演算

Pushing the Boundaries of Tractable Multiperspective Reasoning: A Deduction Calculus for Standpoint EL+

本文提出 Standpoint EL+ 逻辑，通过设计可满足性检查的演绎演算，在保持可处理性的同时扩展表达力，并给出 Datalog 原型实现。