We present an Agent Based Model (ABM) named MIMICS (Modeling Inferential Minds in Conceptual Space), which shows how a social group develops abstract concepts for achieving agreement in communication. Agents describe concepts by assigning properties to them based on learning and communication interactions, trying to develop a conceptual space that discriminates as much as possible between two concepts (i.e., they try to assign properties to concepts decreasing the overlap among the properties that describe them). Contrarily to concrete concepts, those properties come from the social group and not from objects' physical properties. The results show that agents in MIMICS develop abstract concepts that exhibit the same characteristics that are found in studies of real concepts: non -uniform frequency distributions of properties, inter subjective variability and stable concepts that are useful for the simulated social group by providing agreement in communication.