For emerging scientific research domains, local Small Language Models (SLMs) are becoming more attractive, as they offer stronger privacy control and more stable deployment pipelines than Large Language Models. However, in practice, scientific question-answering on SLMs often operates under inevitable constraints: small literature collections, fragmented evidence, limited context window and reasoning abilities. We propose the Evidence-Grounded Typed Knowledge Graph (EGT-KG), a retrieval framework to improve information retrieval with local SLMs. We assessed three question-answering settings: a vanilla Retrieval-Augmented Generation (RAG) workflow and two EGT-KG workflows: an automatically generated relation schema (AS) and an expert-defined relation schema (ES). Our experiments were evaluated with a six-dimensional evaluation framework (S3CRF: Soundness, Correctness, Completeness, Conciseness, Relevance, Fluency) on a Biopolymer-bound Soil Composite literature benchmark, showing that EGT-KG outperforms the vanilla RAG method in most settings, with the best improvement from llama3:8b: a Final Score of 70.37 (+14.67%) and 68.82 (+12.14%) by AS/ES EGT-KG variants.

We introduce a Neural-Symbolic Task Planning framework integrating Large Language Model (LLM) decomposition with category-theoretic verification for resource-aware, temporally consistent planning. Our approach represents states as objects and valid operations as morphisms in a categorical framework, ensuring constraint satisfaction through mathematical pullbacks. We employ bidirectional search that simultaneously expands from initial and goal states, guided by a learned planning distance function that efficiently prunes infeasible paths. Empirical evaluations across three planning domains demonstrate that our method improves completion rates by up to 6.6% and action accuracy by 9.1%, while eliminating resource violations compared to the existing baselines. These results highlight the synergy between LLM-based operator generation and category-theoretic verification for reliable planning in domains requiring both resource-awareness and temporal consistency.