The emergence of large-language models (LLMs) has enabled a new class of semantic data processing systems (SDPSs) to support declarative queries against unstructured documents. Existing SDPSs are, however, lacking a unified algebraic foundation, making their queries difficult to compose, reason, and optimize. We propose a new semantic algebra, SABER (Semantic Algebra Based on Extended Relational algebra), opening the possibility of semantic operations' logical plan construction, optimization, and formal correctness guarantees. We further propose to implement SABER in a SQL-compatible syntax so that it natively supports mixed structured/unstructured data processing. With SABER, we showcase the feasibility of providing a unified interface for existing SDPSs so that it can effectively mix and match any semantically-compatible operator implementation from any SDPS, greatly enhancing SABER's applicability for community contributions.