The emergence of AI-augmented Data Processing Systems (DPSs) has introduced powerful semantic operators that extend traditional data management capabilities with LLM-based processing. However, these systems face fundamental reliability (a.k.a. trust) challenges, as LLMs can generate erroneous outputs, limiting their adoption in critical domains. Existing approaches to LLM constraints--ranging from user-defined functions to constrained decoding--are fragmented, imperative, and lack semantics-aware integration into query execution. To address this gap, we introduce Semantic Integrity Constraints (SICs), a novel declarative abstraction that extends traditional database integrity constraints to govern and optimize semantic operators within DPSs. SICs integrate seamlessly into the relational model, allowing users to specify common classes of constraints (e.g., grounding and soundness) while enabling query-aware enforcement and optimization strategies. In this paper, we present the core design of SICs, describe their formal integration into query execution, and detail our conception of grounding constraints, a key SIC class that ensures factual consistency of generated outputs. In addition, we explore novel enforcement mechanisms, combining proactive (constrained decoding) and reactive (validation and recovery) techniques to optimize efficiency and reliability. Our work establishes SICs as a foundational framework for trustworthy, high-performance AI-augmented data processing, paving the way for future research in constraint-driven optimizations, adaptive enforcement, and enterprise-scale deployments.

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