Lilac: A Modal Separation Logic for Conditional Probability
summary
Lilac presents a separation logic that models probability spaces as heap-like resources and defines an independent combination operator that interprets separating conjunction, yielding a frame rule identical to ordinary separation logic. It encodes mutual independence (including iterated separations), supports continuous random variables, expectations and variances for quantitative proofs, and validates that separating conjunction captures all independence relations. A conditioning modality based on disintegration theory handles conditional probability and the paper formally verifies a weighted sampling algorithm whose correctness hinges on conditional independence.
AI-written summary · about