This paper's aim is to extend horizons in symbolic AI. The key to doing so is to establish a scientific basis for knowledge foundations, and specifically for the concept of meaning, and its computation. This led to the creation of the Meaning Computation AI (MCAI). Knowledge structures are at the heart of MCAI. The semantic triple chain, one of such structures, is the subject of this paper. This structure is the core of introducing computational semantic reasoning models across a variety of domains. To efficiently apply knowledge structures to create semantic reasoning applications MCAI contains a development framework consisting of four components. The first component stems from our discovery that knowledge is relational in nature. It can be expressed through implicit relations (which reflect meaning) and semantic relations (which describe how implicit relations act between entities). An algebraical apparatus for relational knowledge, specifically for implicit and semantic relations, represents the first component. Axiomatic models of relational domain ontologies and domain-oriented semantic reasoning models comprise the second and third components. The fourth component contains domain-oriented semantic reasoning engines.