As Distributed Ledger Technologies (DLTs) mature, the inherent performance and scalability shortcomings of linearly structured blockchain designs become better understood. Protocols based on Directed Acyclic Graphs (DAGs) have been proposed to address such shortcomings. DAG-based protocols differ from traditional DLTs in the way they build and represent knowledge about transactions and relations between them. While traditional DLTs have straightforward homogeneous semantic attached to blocks and links between blocks, the semantic of vertices and edges in DAG-based protocols is nuanced and varied. In this work, we identify almost a dozen of knowledge-building dimensions in DAG-based DLTs, none of which have been studied before. Knowledge-building is important in DAG-based DLTs because of its significant impact on the size of the DAG, the pace at which new transactions are added, the finality of transactions, and so on. We analyze 40 DAG-based DLTs from this perspective, summarize our results in a taxonomy, and identify a number of research gaps.