As early as 1949, Weaver defined communication in a very broad sense to include all procedures by which one mind or technical system can influence another, thus establishing the idea of semantic communication. With the recent success of machine learning in expert assistance systems where sensed information is wirelessly provided to a human to assist task execution, the need to design effective and efficient communications has become increasingly apparent. In particular, semantic communication aims to convey the meaning behind the sensed information relevant for Human Decision-Making (HDM). Regarding the interplay between semantic communication and HDM, many questions remain, such as how to model the entire end-to-end sensing-decision-making process, how to design semantic communication for the HDM and which information should be provided for HDM. To address these questions, we propose to integrate semantic communication and HDM into one probabilistic end-to-end sensing-decision framework that bridges communications and psychology. In our interdisciplinary framework, we model the human through a HDM process, allowing us to explore how feature extraction from semantic communication can best support HDM both in theory and in simulations. In this sense, our study reveals the fundamental design trade-off between maximizing the relevant semantic information and matching the cognitive capabilities of the HDM model. Our initial analysis shows how semantic communication can balance the level of detail with human cognitive capabilities while demanding less bandwidth, power, and latency.