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Owing to the results of research in system science, artificial intelligence, and cognitive engineering, engineered systems are becoming more and more powered by knowledge. Complementing common-sense and scientific knowledge, system knowledge is maturing into a crucial productive asset. However, an overall theory of the knowledge of intellectualized systems does not exist. Some researchers suggest that time has come to establish a philosophically underpinned theoretical framework. This motion is seconded by the on-going intelligence revolution, in which artificial intelligence becomes a productive power, enabler of smart systems, and a strong transformer of the social life. The goal of this paper is to propose a skeleton of the needed generic theory of system knowledge (and a possible new branch of philosophical studies). The major assumption is that a significant part of the synthetic system knowledge (SSK) is “sympérasma”, that is, knowledge conjectured, inferred, constructed, or otherwise derived during the operation of systems. This part will become even more dominant in the future. Starting out from the above term, the paper suggests calling this theory “sympérasmology”. Some specific domains of “sympérasmological” studies, such as (i) manifestations of SSK, (ii) mechanisms of generating SSK, (iii) dependability of SSK, (iv) operational power of SSK, (v) composability of SSK, and (vi) advancement of SSK, are identified. It is understood that the essence and status of SSK cannot be investigated without considering the related cognitive processes and technological enablers. The paper presents a number of open questions relevant for follow-up discussions. Full article