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The authors propose a new approach to the integration of functional and logic languages, based on a theory of unification and set valued functions. A set-valued function maps a tuple of input sets into an output set. This document a language called Setlog illustrates this approach, and gives its model-theoretic, fixed-point, and operational semantics. The model-theoretic semantics and fixed-point semantics resemble that of Horn logic. The operational semantics uses outermost reduction (for set-valued functions) and unification (for terms). The correctness of the operational semantics is established through soundness and completeness proofs. Keywords: Syntax; Set theory.