In the definition of the class CQ of computable queries, Chandra and Harel ([7]) included untyped queries, that is, queries whose answers are relations of possibly different arities on different databases. However, it seems that in the work which followed on the subject, untyped queries were not considered at all, neither in the abstract machines side nor in the logic framework. We propose to re-introduce these queries in the study of Query Computability, and also in the construction of Industry query languages, without leaving the Relational Model. So, we define an extension of the Reflective Relational Machine of [2], which we call untyped Reflective Relational Machine. In the logic framework, we define a new quantifier, which we call conditional quantifier, and we build with it an infinitary logic which we denote by . Then we prove completeness results regarding both formalisms considering both typed and untyped queries.