PRAXA: A Grammar for What-If Analysis

What-if analysis is widely used to explore hypothetical scenarios and evaluate alternative pathways to desired results. However, current approaches are fragmented: systems implement what-if capabilities under diverse terminologies with different analytic techniques. Such fragmentation limits expressiveness, impedes flexible composition and reuse of workflows, and hinders tighter integration with AI. We present PRAXA, a compositional grammar of what-if analysis derived from recurring patterns across 141 publications in visual analytics and HCI venues. PRAXA formulates three primitives: (1) data, defining variables under analysis, (2) model, specifying predictive mechanisms, and (3) interaction operations-pairs of user actions and system responses that execute analyses. We encode PRAXA into a declarative specification language, PSL. To evaluate PRAXA, we first show expressiveness by reconstructing representative workflows from prior work as structured compositions, exposing the predominant focus on single-step rather than multi-step reasoning. Second, we demonstrate composability by revealing that capabilities described under distinct terminologies share the same grammatical structure with different parameterizations, and that new multi-step workflows emerge through composition. Third, we illustrate PSL as an intermediate representation for translating natural-language what-if queries into executable interactive interfaces, enabling inspection, validation, and more transparent AI integration. By unifying diverse what-if approaches as a grammar, PRAXA provides a foundation for analyzing, composing, and supporting workflows in next-generation what-if systems.