The Review Algebra

Semantic assertions produced by human and computational processes may be provisional, contested, corroborated, falsified, deferred, or replaced, while their subsequent use may depend on explicit policies determining what is sufficiently stabilised for a particular purpose. This paper develops the Review Algebra, a formal and computational framework for representing these transformations while preserving the provenance-bearing activities through which semantic assertions are generated, examined, and admitted to subsequent semantic states. The algebra distinguishes three recurring operations: candidate generation, review, and finalisation. Candidate generation makes semantic assertions available for consideration without implying their acceptance. Review examines candidate assertions and returns semantic values together with explicit statuses describing what happened to the candidates. Finalisation applies a policy determining which reviewed assertions enter a subsequent stabilised semantic state. Observation and inference are treated as distinct mechanisms of candidate generation rather than additional operators of the algebra. Other mechanisms may include reconciliation, federation, import, computational analysis, or human proposal. Their epistemic differences remain represented through provenance while their outputs participate in the same downstream review structure. The Review Algebra extends ordinary relational and tidy data operations rather than replacing them. Wide and long review workspaces provide computational and human-facing projections over persistent assertions and activities without becoming the canonical knowledge model. Stabilised assertions can subsequently participate in further candidate generation, making semantic stabilisation a recursive, provenance-bearing transformation between reviewable semantic states. The Review Algebra provides the underlying formalisation for a broader framework of human-centred semantic knowledge production. It deliberately does not prescribe the epistemology of observation, interpretation, reconciliation, or specialist judgement. Instead, it provides a common computational structure through which assertions produced by heterogeneous human and computational activities can remain reviewable, provenance-bearing, and reusable.