A set of views defined by selection queries splits a database relation into sub-relations, each containing a subset of the original rows. This decomposition into horizontal fragments is lossless when the initial relation can be reconstructed from the fragments by union. In this paper, we consider horizontal decomposition in a setting where some of the attributes in the database schema are interpreted over a specific domain, on which a set of special predicates and functions is defined. We study losslessness in the presence of integrity constraints on the database schema. We consider the class of conditional domain constraints (CDCs), which restrict the values that the interpreted attributes may take whenever a certain condition holds on the non-interpreted ones, and investigate lossless horizontal decomposition under CDCs in isolation, as well as in combination with functional and unary inclusion dependencies.