Formal Concept Analysis (FCA) is a mathematically inspired field of knowledge representation with wide applications in knowledge discovery and decision support. Polyadic FCA is a generalization of classical FCA that instead of a binary uses an arbitrary, n-ary incidence relation to define formal concepts, i.e., data clusters in which all elements are interrelated. We discuss a paradigm for navigating the space of such (formal) concepts, based on so-called membership constraints. We present an implementation for the cases $$n\in \{2,3,4\}$$ using an encoding into answer-set programming (ASP) allowing us to exploit highly efficient strategies offered by optimized ASP solvers. For the case $$n=3$$, we compare this implementation to a second strategy that uses exhaustive search in the concept set, which is precomputed by an existing tool. We evaluate the implementation strategies in terms of performance. Finally, we discuss the limitations of each approach and the possibility of generalizations to n-ary datasets.