Abstract: In order to enhance the understanding of the essence of safety events in safety scientific researches, mathematical expression was researched for the intension of safety events based on the safety structure theory. Intrinsic factors in safety events were defined, and a processing algorithm was proposed for obtaining the intrinsic factors set by factors reduction, factors set completeness test and factors independence test. A definition of the intension of the safety events was given from the perspective of the logic. A mathematical expression was worked out for the intension of safety events based on the membership function of representation extension of intrinsic factors. The research show that the intrinsic factors set of a safety event consists of all independent and complete factors determining the occurrence of the safety event, and the intension of a safety event is the combination of the attributes of all intrinsic factors of the safety event, and that the factor space of a safety event is constituted by the cartesian product set of the states sets of all the intrinsic factors, and is the mathematical logic analysis framework to describe the intension of the safety event.

Key words: intension of safety events, intrinsic factor, factor attribute, representation extension, safety structure theory, factor spaces theory