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Towards objective Bayesian foundations with fuzzy events

We present an axiomatic approach to conditional measures of fuzzy events which is inspired by the Dupre�Tipler argument for Bayesianism. Unlike there or in the older and related Cox argument, although we are able to derive additive probabilities other non-additive solutions exist. Our motivation is to show that Bayesian foundational arguments are based on Boolean logic but they do not require it and may be based on fuzzy logic instead.