Individual productivity is a key determinant of organizational performance and employee well-being, yet its underlying drivers are inherently multi-factorial and context-dependent. Existing productivity support systems typically monitor environmental, physiological, or behavioural factors in isolation, limiting their ability to provide personalized and explainable interventions. This paper presents ADAPTS, an adaptive Knowledge Graph (KG)-driven smart system for incentive-based supporting workplace productivity. The proposed framework integrates indoor environmental measurements, wearable-derived physiological and behavioural indicators, and questionnaire-based user profiles into an RDF/OWL Knowledge Graph. A rule-based reasoning layer enriches the graph with high-level semantic knowledge and computes a multi-factor Daily Productivity Score (DPS). The enriched graph is subsequently exploited through a Graph Retrieval-Augmented Generation (GraphRAG) mechanism to construct a Unified User Context that grounds a Large Language Model (LLM) for generating personalized behavioural interventions and adaptive incentive strategies. User interactions are continuously incorporated into the Knowledge Graph, enabling iterative personalization through a closed feedback loop. The proposed framework was evaluated using data collected from 25 participants. Experimental results show that KG-grounded recommendations were consistently preferred over non-grounded LLM recommendations, achieving higher scores in perceived relevance, personalization, explainability, and user trust. These findings demonstrate the effectiveness of combining semantic knowledge representation, graph reasoning, and generative AI to deliver personalized and explainable recommendations targeting environmental, physiological, and behavioural conditions associated with workplace productivity.