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Commonsense Reasoning (CSR) and Commonsense Knowledge (CSK) (together abbreviated as CSRK) are areas of study concerned with problems which are trivially easy for adults but which are challenging for artificial systems. This paper describes how the SP System—meaning the SP Theory of Intelligence and its realisation in the SP Computer Model—has strengths and potential in several aspects of CSRK. A particular strength of the SP System is that it shows promise as an overarching theory for four areas of relative success with CSRK problems—described by other authors—which have been developed without any integrative theory. How the SP System may help to solve four other kinds of CSRK problem is described: 1) how the strength of evidence for a murder may be influenced by the level of lighting of the murder as it was witnessed; 2) how people may arrive at the commonly- accepted interpretation of phrases like “water bird”; 3) interpretation of the horse’s head scene in “The Godfather” film; and 4) how the SP System may help to resolve the reference of an ambiguous pronoun in sentences in the format of a ‘Winograd schema’. Also described is why a fifth CSRK problem—modelling how a cook may crack an egg into a bowl—is beyond the capabilities of the SP System as it is now and how those deficiencies may be overcome via planned developments of the system.