LLM-based chat systems have become valuable tools for design practice, enabling rapid ideation and flexible task support. Yet these systems process designer utterances as generic sequences, maintaining context through recency rather than through any model of how the speaker organizes knowledge. In design conversation, this gap compounds as relational context decays between turns, identical words go unresolved across designers, and the conversation loops or restarts rather than deepens. We present CogChat, a real-time chat framework that grounds conversational AI in a personal heterogeneous knowledge graph constructed from each designer's input. The system extracts typed entities and relations into a heterogeneous graph, then applies a HGT (Heterogeneous Graph Transformer) to select structurally relevant nodes for response generation and to generate both intentional and exploratory probing questions. Technical evaluation shows that HGT-based entity selection outperforms both ungrounded LLM interaction and naive KG augmentation, which introduces noise that degrades response quality. A within-subjects study with nine professional designers indicates that grounding conversation in a relationally structured, designer-specific semantic context improves context retention, personalized intent interpretation, and conversational depth while reducing cognitive load. These findings suggest that structuring a designer's expressed concepts and relations as a dynamic knowledge graph can preserve relational context that fades across turns, pointing toward a graph-grounded approach to long-term context management in LLM-based interaction.

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