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Computational humor is a subdiscipline of computational linguistics with applications in human computer interfaces, edutainment, affective computing, intelligent agents, and other areas. Based on ontological semantics, we develop the resources and algorithms the computer needs to understand and produce humor, in principle and on a detailed example. Our ultimate output will not be that of a toy system that fills in templates, previously the only available approach, but rather true natural language generation, based on the computer approximation of the human understanding of the joke. This paper shows how ontological semantics provides for and computes the full computer understanding of humor, a sine qua non of humor generation.