We present a formal study of semantics for relational programming language miniKanren. First, we formulate denotational semantics which corresponds to the minimal Herbrand model for definite logic programs. Second, we present operational semantics which models the distinctive feature of miniKanren implementation — interleaving, — and prove its soundness and completeness w.r.t. the denotational semantics. Our development is supported by a Coq specification, from which a reference interpreter can be extracted. We also derive from our main result a certified semantics (and a reference interpreter) for SLD resolution with cut and prove its soundness.