A new concept of a multi-valued associative memory is introduced, generalizing a similar one in fuzzy neural networks. We expand the results on fuzzy associative memory with thresholds, to the case of a multi-valued one: we introduce the novel concept of such a network without numbers, investigate its properties, and give a learning algorithm in the multi-valued case. We discovered conditions under which it is possible to store given pairs of network variable patterns in such a multi-valued associative memory. In the multi-valued neural network, all variables are not numbers, but elements or subsets of a lattice, i.e., they are all only partially-ordered. Lattice operations are used to build the network output by inputs. In this paper, the lattice is assumed to be Brouwer and determines the implication used, together with other lattice operations, to determine the neural network output. We gave the example of the network use to classify aircraft/spacecraft trajectories.