Xiaoqian Wu Shanghai Jiao Tong University enlighten@sjtu.edu.cn In Tab. 1, we conclude the notations in this work for clarity.Notation Definition r A rule. The size of the premise symbols set M . S is the symbol set, and R is the rule set. A \ B The set difference of A and B. D A very large-scale activity images database.

Human reasoning can be understood as a cooperation between the intuitive, associative "System-1" and the deliberative, logical "System-2".

Human reasoning can be understood as a cooperation between the intuitive, associative System-1'' and the deliberative, logical System-2''. For existing System-1-like methods in visual activity understanding, it is crucial to integrate System-2 processing to improve explainability, generalization, and data efficiency. One possible path of activity reasoning is building a symbolic system composed of symbols and rules, where one rule connects multiple symbols, implying human knowledge and reasoning abilities.Previous methods have made progress, but are defective with limited symbols from handcraft and limited rules from visual-based annotations, failing to cover the complex patterns of activities and lacking compositional generalization. To overcome the defects, we propose a new symbolic system with two ideal important properties: broad-coverage symbols and rational rules. Collecting massive human knowledge via manual annotations is expensive to instantiate this symbolic system.

This paper synthesizes a series of formal proofs to construct a unified theory on the logical limits of the Symbol Grounding Problem. We distinguish between internal meaning (sense), which formal systems can possess via axioms, and external grounding (reference), which is a necessary condition for connecting symbols to the world. We demonstrate through a four-stage argument that meaningful grounding within a formal system must arise from a process that is external, dynamic, and non-fixed algorithmic. First, we show that for a purely symbolic system, the impossibility of grounding is a direct consequence of its definition. Second, we extend this limitation to systems with any finite, static set of pre-established meanings (Semantic Axioms). By formally modeling the computationalist hypothesis-which equates grounding with internal derivation-we prove via Gödelian arguments that such systems cannot consistently and completely define a "groundability predicate" for all truths. Third, we demonstrate that the "grounding act" for emergent meanings cannot be inferred from internal rules but requires an axiomatic, meta-level update. Drawing on Turing's concept of Oracle Machines and Piccinini's analysis of the mathematical objection, we identify this update as physical transduction. Finally, we prove that this process cannot be simulated by a fixed judgment algorithm, validating the logical necessity of embodied interaction.

Word sense disambiguation is a fundamental challenge in natural language understanding. Current methods are primarily aimed at coarse-grained representations (e.g. WordNet synsets or FrameNet frames) and require hand-annotated training data to construct. This makes it difficult to automatically disambiguate richer representations (e.g. built on OpenCyc) that are needed for sophisticated inference. We propose a method that uses statistical language models as oracles for disambiguation that does not require any hand-annotation of training data. Instead, the multiple candidate meanings generated by a symbolic NLU system are converted into distinguishable natural language alternatives, which are used to query an LLM to select appropriate interpretations given the linguistic context. The selected meanings are propagated back to the symbolic NLU system. We evaluate our method against human-annotated gold answers to demonstrate its effectiveness.

Agentic AI represents a transformative shift in artificial intelligence, but its rapid advancement has led to a fragmented understanding, often conflating modern neural systems with outdated symbolic models -- a practice known as conceptual retrofitting. This survey cuts through this confusion by introducing a novel dual-paradigm framework that categorizes agentic systems into two distinct lineages: the Symbolic/Classical (relying on algorithmic planning and persistent state) and the Neural/Generative (leveraging stochastic generation and prompt-driven orchestration). Through a systematic PRISMA-based review of 90 studies (2018--2025), we provide a comprehensive analysis structured around this framework across three dimensions: (1) the theoretical foundations and architectural principles defining each paradigm; (2) domain-specific implementations in healthcare, finance, and robotics, demonstrating how application constraints dictate paradigm selection; and (3) paradigm-specific ethical and governance challenges, revealing divergent risks and mitigation strategies. Our analysis reveals that the choice of paradigm is strategic: symbolic systems dominate safety-critical domains (e.g., healthcare), while neural systems prevail in adaptive, data-rich environments (e.g., finance). Furthermore, we identify critical research gaps, including a significant deficit in governance models for symbolic systems and a pressing need for hybrid neuro-symbolic architectures. The findings culminate in a strategic roadmap arguing that the future of Agentic AI lies not in the dominance of one paradigm, but in their intentional integration to create systems that are both adaptable and reliable. This work provides the essential conceptual toolkit to guide future research, development, and policy toward robust and trustworthy hybrid intelligent systems.

Optimizing Register Transfer Level (RTL) code is crucial for improving the power, performance, and area (PPA) of digital circuits in the early stages of synthesis. Manual rewriting, guided by synthesis feedback, can yield high-quality results but is time-consuming and error-prone. Most existing compiler-based approaches have difficulty handling complex design constraints. Large Language Model (LLM)-based methods have emerged as a promising alternative to address these challenges. However, LLM-based approaches often face difficulties in ensuring alignment between the generated code and the provided prompts. This paper presents SymRTLO, a novel neuron-symbolic RTL optimization framework that seamlessly integrates LLM-based code rewriting with symbolic reasoning techniques. Our method incorporates a retrieval-augmented generation (RAG) system of optimization rules and Abstract Syntax Tree (AST)-based templates, enabling LLM-based rewriting that maintains syntactic correctness while minimizing undesired circuit behaviors. A symbolic module is proposed for analyzing and optimizing finite state machine (FSM) logic, allowing fine-grained state merging and partial specification handling beyond the scope of pattern-based compilers. Furthermore, a fast verification pipeline, combining formal equivalence checks with test-driven validation, further reduces the complexity of verification. Experiments on the RTL-Rewriter benchmark with Synopsys Design Compiler and Yosys show that SymRTLO improves power, performance, and area (PPA) by up to 43.9%, 62.5%, and 51.1%, respectively, compared to the state-of-the-art methods.

Some of the strongest evidence that human minds should be thought about in terms of symbolic systems has been the way they combine ideas, produce novelty, and learn quickly. We argue that modern neural networks -- and the artificial intelligence systems built upon them -- exhibit similar abilities. This undermines the argument that the cognitive processes and representations used by human minds are symbolic, although the fact that these neural networks are typically trained on data generated by symbolic systems illustrates that such systems play an important role in characterizing the abstract problems that human minds have to solve. This argument leads us to offer a new agenda for research on the symbolic basis of human thought.