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This dissertation proposes a novel hybrid neuro-symbolic model that integrates Logical Neural Networks (LNNs) with Echo State Networks (ESNs) to enhance logical reasoning and temporal adaptability in complex systems. LNNs provide a differentiable framework for incorporating symbolic logic into neural architectures – every neuron corresponds to a logical formula component, enabling interpretable reasoning and robust handling of knowledge. ESNs, a form of reservoir computing, contribute a dynamic “memory” through a fixed, randomly connected recurrent layer (the reservoir) that projects inputs into high-dimensional state representations. Coupling these paradigms synergistically combines the strengths of symbolic logic with those of neural networks, overcoming key limitations of each.
The versatility of the LNN–ESN hybrid is demonstrated across three distinct domains: cybersecurity, robotics, and natural language processing (NLP). In cybersecurity, we develop an advanced Intrusion Detection System (IDS) that leverages the hybrid model to detect network intrusions. The LNN component encodes expert security rules and logical constraints, while the ESN learns temporal patterns of network traffic, together improving detection accuracy and significantly reducing false alarms by combining signature-based and anomaly-based detection. In robotics, we apply the model to temporal logic reasoning tasks, where autonomous agents satisfy Linear Temporal Logic (LTL) specifications. The ESN’s reservoir captures temporal context from sensor inputs, and the LNN infuses logical constraints, enabling robots to conform to complex task specifications over time. In NLP, we illustrate how the hybrid model can maintain logical consistency in language understanding and reasoning. By remembering sequential context (ESN) and applying formal logical rules (LNN) to that context, the model adeptly handles tasks like structured text inference and multi-turn dialogue with improved coherence, addressing known limitations of purely neural language models in logical reasoning.
The research shows that the LNN–ESN hybrid achieves state-of-the-art performance in each domain, exceeding the accuracy of conventional deep learning and other neuro-symbolic techniques, while offering explainable insights into its decisions. The introduction of logical constraints into the temporal dynamics of ESN yields accurate models that are verifiable against domain knowledge (e.g. security policies, formal logic rules). Key contributions of this dissertation include: (1) the design of a unified LNN–ESN architecture and learning algorithm; (2) empirical demonstration of its generalizability across heterogeneous domains; (3) enhancements to intrusion detection and robot planning via integrated logic-based reasoning; and (4) comparative analyses showing the hybrid model’s superiority over existing hybrid AI approaches in adaptability and interpretability. The broader significance lies in advancing neuro-symbolic AI as a practical paradigm. Finally, we discuss limitations and provide a roadmap for future work to extend the model’s scalability and usability, laying the groundwork for next-generation AI systems.