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  1. Angelo Gilio & Giuseppe Sanfilippo (2014). Conditional Random Quantities and Compounds of Conditionals. Studia Logica 102 (4):709-729.
    In this paper we consider conditional random quantities (c.r.q.’s) in the setting of coherence. Based on betting scheme, a c.r.q. X|H is not looked at as a restriction but, in a more extended way, as \({XH + \mathbb{P}(X|H)H^c}\) ; in particular (the indicator of) a conditional event E|H is looked at as EH + P(E|H)H c . This extended notion of c.r.q. allows algebraic developments among c.r.q.’s even if the conditioning events are different; then, for instance, we can give a (...)
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  2. Angelo Gilio & Giuseppe Sanfilippo (2013). Conjunction, Disjunction and Iterated Conditioning of Conditional Events. In R. Kruse (ed.), Advances in Intelligent Systems and Computing. Springer.
    Starting from a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity, whose set of possible values normally contains the probabilities assessed for the two conditional events. We examine some cases of logical dependencies, where the conjunction is a conditional event; moreover, we give the (...)
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  3. Angelo Gilio (2005). Probabilistic Logic Under Coherence, Conditional Interpretations, and Default Reasoning. Synthese 146 (1-2):139 - 152.
    We study a probabilistic logic based on the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence). We examine probabilistic conditional knowledge bases associated with imprecise probability assessments defined on arbitrary families of conditional events. We introduce a notion of conditional interpretation defined directly in terms of precise probability assessments. We also examine a property of strong satisfiability which is related to the notion of toleration well known in default reasoning. In our framework we give more (...)
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  4. Veronica Biazzo, Angelo Gilio, Thomas Lukasiewicz & Giuseppe Sanfilippo (2002). Probabilistic Logic Under Coherence, Model-Theoretic Probabilistic Logic, and Default Reasoning in SystemP. Journal of Applied Non-Classical Logics 12 (2):189-213.
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  5. Giulianella Coletti, Angelo Gilio & Romano Scozzafava (1993). Comparative Probability for Conditional Events: A New Look Through Coherence. Theory and Decision 35 (3):237-258.
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  6. Giulianella Coletti, Angelo Gilio & Romano Scozzafava (1991). Conditional Events with Vague Information in Expert Systems. In B. Bouchon-Meunier, R. R. Yager & L. A. Zadeh (eds.), Uncertainty in Knowledge Bases. Springer. 106--114.
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