LLM-MatLogic: Executable Exchange Contracts for Knowledge-Graph Query Answering with Scoped Negation

LLM-to-KG systems frequently fail on exclusion-rich questions because natural-language negation is both scope-sensitive and evidence-dependent: it may constrain only one subgoal/branch and only certain supporting paths, yet such attachment is rarely explicit in text. We propose the Executable Exchange Contract (EEC) to bridge this gap, specifying scope-bound exclusions as executable control metadata exchanged between a specifier and an executor. Our executor, MatLogic, compiles exclusions into scope-local masks applied during multi-hop propagation and executes requests under a unified P$\rightarrow$N$\rightarrow$C/D schedule, ensuring exclusions are enforced before witness loss and branch entanglement. The system can also return compact witness pointers to keep support types distinguishable when needed. We evaluate on both structured complex queries and end-to-end natural-language KGQA, and introduce contract-aligned diagnostics that isolate errors from specification versus execution and verify the necessity of scoped enforcement.