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• W2975548398 abstract "We deepen the study of conjoined and disjoined conditional events in the setting of coherence. These objects, differently from other approaches, are defined in the framework of conditional random quantities. We show that some well known properties, valid in the case of unconditional events, still hold in our approach to logical operations among conditional events. In particular we prove a decomposition formula and a related additive property. Then, we introduce the set of conditional constituents generated by $n$ conditional events and we show that they satisfy the basic properties valid in the case of unconditional events. We obtain a generalized inclusion-exclusion formula and we prove a suitable distributivity property. Moreover, under logical independence of basic unconditional events, we give two necessary and sufficient coherence conditions. The first condition gives a geometrical characterization for the coherence of prevision assessments on a family $mathscr{F}$ constituted by $n$ conditional events and all possible conjunctions among them. The second condition characterizes the coherence of prevision assessments defined on $mathscr{F}cup mathscr{K}$, where $mathscr{K}$ is the set of conditional constituents associated with the conditional events in $mathscr{F}$. Then, we give a further theoretical result and we examine some examples and counterexamples. Finally, we make a comparison with other approaches and we illustrate some theoretical aspects and applications." @default.
• W2975548398 created "2019-10-03" @default.
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• W2975548398 date "2020-11-01" @default.
• W2975548398 modified "2023-10-17" @default.
• W2975548398 title "Algebraic aspects and coherence conditions for conjoined and disjoined conditionals" @default.
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• W2975548398 doi "https://doi.org/10.1016/j.ijar.2020.08.004" @default.
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