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This article presents a logical formalization of the emotional appraisal theory, i.e., it formalizes the cognitive process of evaluation that elicits an emotion. This formalization is psychologically grounded on the OCC cognitive model of emotions. More specifically, we are interested in event-based emotions, i.e., emotions that are elicited by the evaluation of the consequences of an event that either happened or will happen. The formal modelling presented here is based on the AfPL Probabilistic Logic, a BDI-like probabilistic modal logic, which allows our model to verify whether the variables that determine the elicitation of emotions achieved the necessary threshold or not. The proposed logical formalization aims at addressing how the emotions are elicited by the agent cognitive mental states (desires, beliefs and intentions), and how to represent the intensity of the emotions. These are important initial points in the investigation of the dynamic interaction among emotions and other mental states.