All the code and data are open-sourced at our website.

Bridging continuous perceptual signals and discrete symbolic reasoning is a fundamental challenge in AI systems that must operate under uncertainty. We present a neuro-symbolic framework that explicitly models and propagates uncertainty from perception to planning, providing a principled connection between these two abstraction levels. Our approach couples a transformer-based perceptual front-end with graph neural network (GNN) relational reasoning to extract probabilistic symbolic states from visual observations, and an uncertainty-aware symbolic planner that actively gathers information when confidence is low. We demonstrate the framework's effectiveness on tabletop robotic manipulation as a concrete application: the translator processes 10,047 PyBullet-generated scenes (3--10 objects) and outputs probabilistic predicates with calibrated confidences (overall F1=0.68). When embedded in the planner, the system achieves 94\%/90\%/88\% success on Simple Stack, Deep Stack, and Clear+Stack benchmarks (90.7\% average), exceeding the strongest POMDP baseline by 10--14 points while planning within 15\,ms. A probabilistic graphical-model analysis establishes a quantitative link between calibrated uncertainty and planning convergence, providing theoretical guarantees that are validated empirically. The framework is general-purpose and can be applied to any domain requiring uncertainty-aware reasoning from perceptual input to symbolic planning.

Recent years have witnessed the rapid development of Neuro-Symbolic (NeSy) AI systems, which integrate symbolic reasoning into deep neural networks. However, most of the existing benchmarks for NeSy AI fail to provide long-horizon reasoning tasks with complex multi-agent interactions. Furthermore, they are usually constrained by fixed and simplistic logical rules over limited entities, making them far from real-world complexities. To address these crucial gaps, we introduce LogiCity, the first simulator based on customizable first-order logic (FOL) for an urban-like environment with multiple dynamic agents. LogiCity models diverse urban elements using semantic and spatial concepts, such as IsAmbulance(X) and IsClose(X, Y). These concepts are used to define FOL rules that govern the behavior of various agents. Since the concepts and rules are abstractions, they can be universally applied to cities with any agent compositions, facilitating the instantiation of diverse scenarios. Besides, a key feature of LogiCity is its support for user-configurable abstractions, enabling customizable simulation complexities for logical reasoning. To explore various aspects of NeSy AI, LogiCity introduces two tasks, one features long-horizon sequential decision-making, and the other focuses on one-step visual reasoning, varying in difficulty and agent behaviors. Our extensive evaluation reveals the advantage of NeSy frameworks in abstract reasoning. Moreover, we highlight the significant challenges of handling more complex abstractions in long-horizon multi-agent scenarios or under high-dimensional, imbalanced data. With its flexible design, various features, and newly raised challenges, we believe LogiCity represents a pivotal step forward in advancing the next generation of NeSy AI. All the code and data are open-sourced at our website.

To talk about Reasoning, it's important to understand how we got here. This article covers what I call the pre-history of Classical AI -- those parts of the story that happened before the invention of modern computers (pre 1950s) but are crucial to understanding why we believe that AI is possible. This is part 2 in a series on Reasoning. Like most things, the very beginnings of classical AI is rooted in philosophy, and starts in the ancient world (the Greeks, Indians, and Chinese all had some early forms of logic). But, as I'm not a masochist we start in more contemporary times with two big ideas that lay the foundation for modern AI: The development of logic was humanity's first great attempt at mechanizing intelligence, and the basis for modern logic lies with George Boole, Charles Pierce, and Gottlob Frege.

Inductive logic programming, or relational learning, is a powerful paradigm for machine learning or data mining. However, in order for ILP to become practically useful, the efficiency of ILP systems must improve substantially. To this end, the notion of a query pack is introduced: it structures sets of similar queries. Furthermore, a mechanism is described for executing such query packs. A complexity analysis shows that considerable efficiency improvements can be achieved through the use of this query pack execution mechanism. This claim is supported by empirical results obtained by incorporating support for query pack execution in two existing learning systems.