We analyse perception and memory, using mathematical models for knowledge graphs and tensors, to gain insights into the corresponding functionalities of the human mind. Our discussion is based on the concept of propositional sentences consisting of \textit{subject-predicate-object} (SPO) triples for expressing elementary facts. SPO sentences are the basis for most natural languages but might also be important for explicit perception and declarative memories, as well as intra-brain communication and the ability to argue and reason. A set of SPO sentences can be described as a knowledge graph, which can be transformed into an adjacency tensor. We introduce tensor models, where concepts have dual representations as indices and associated embeddings, two constructs we believe are essential for the understanding of implicit and explicit perception and memory in the brain. We argue that a biological realization of perception and memory imposes constraints on information processing. In particular, we propose that explicit perception and declarative memories require a semantic decoder, which, in a simple realization, is based on four layers: First, a sensory memory layer, as a buffer for sensory input, second, an index layer representing concepts, third, a memoryless representation layer for the broadcasting of information ---the "blackboard", or the "canvas" of the brain--- and fourth, a working memory layer as a processing center and data buffer. We discuss the operations of the four layers and relate them to the global workspace theory. In a Bayesian brain interpretation, semantic memory defines the prior for observable triple statements. We propose that ---in evolution and during development--- semantic memory, episodic memory, and natural language evolved as emergent properties in agents' process to gain a deeper understanding of sensory information.

We analyze the close link between perception and memory. Our main hypothesis is that some of the main memory systems of the human brain, e.g., the episodic memory, the semantic memory, and to some degree also the working memory, are by-products of the need for humans to gradually extract more meaningful and more complex information from sensory inputs. Our model is an extension to the tensor memory approach. The key notions are index representations for entities, concepts, relationships and time instances, embeddings associated with the indices, a working memory layer, and a sensory memory layer. Perception and memory are realized as an interplay between the different layers. Our model is both competitive to other technical solutions and, as we argue, biologically plausible. Our experiments demonstrate that semantic memory can evolve from perception as a distinguishable functional module.