Owing to the developments of the distributed system and the internet, knowledge is more effective for workings of many types. The stream media for seminar class and retrieval from knowledge base are more necessary in relations to learning process. We aim at a design of IoT software, as interactive computing, concerned with seminar streams and retrieval derivations from queries in knowledge base. The IoT tool involves a human interface of interaction to virtual reality seminar, as well as to retrievals from queries regarding specified knowledge based on algebraic relations. Such human interface takes into a formal shape as interactive computing for working with the internet. With respect to semantics for interactive computing, this paper is concerned with algebraic structures of stream media and retrieval from knowledge base. As regards stream sequence for organization of seminar series, we extend the rewriting rules of a state grammar, controlled by states (abstractly for human interaction). For knowledge and acquisition, requisite relations with exceptions are compactly organized for queries. The elaborate model of knowledge base may be formally described, with retrieval derivations, so that the retrieval may be procedural and implementable. For descriptions of IoT software, we think of object-oriented program classes as feasible. The meaning of IoT tools can be captured for interactive computing as behaviors in abstract state space, implicitly in relation to modal logic semantics.