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Giuseppe Sanfilippo
Università degli Studi di Palermo
  1.  50
    Conditional Random Quantities and Compounds of Conditionals.Angelo Gilio & Giuseppe Sanfilippo - 2014 - 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.  28
    Generalized Logical Operations Among Conditional Events.Angelo Gilio & Giuseppe Sanfilippo - 2019 - Applied Intelligence 49:79-102.
    We generalize, by a progressive procedure, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. In our coherence-based approach, conjunctions and disjunctions are suitable conditional random quantities. We define the notion of negation, by verifying De Morgan’s Laws. We also show that conjunction and disjunction satisfy the associative and commutative properties, and a monotonicity property. Then, we give some results on coherence of prevision assessments for some families of compounded conditionals; in particular (...)
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  3.  41
    Transitivity in Coherence-Based Probability Logic.Angelo Gilio, Niki Pfeifer & Giuseppe Sanfilippo - 2016 - Journal of Applied Logic 14:46-64.
    We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Moreover, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases. Finally, we apply our results to study selected probabilistic (...)
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  4. Conjunction, Disjunction and Iterated Conditioning of Conditional Events.Angelo Gilio & Giuseppe Sanfilippo - 2013 - 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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  5.  52
    Probabilistic Logic Under Coherence, Model-Theoretic Probabilistic Logic, and Default Reasoning in System P.Veronica Biazzo, Angelo Gilio, Thomas Lukasiewicz & Giuseppe Sanfilippo - 2002 - Journal of Applied Non-Classical Logics 12 (2):189-213.
    We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore how probabilistic reasoning under coherence is related to model- theoretic probabilistic reasoning and to default reasoning in System . In particular, we show that the notions of g-coherence and of g-coherent entailment can be expressed by combining notions in model-theoretic probabilistic logic with concepts from default reasoning. Moreover, we show that probabilistic reasoning under coherence is a generalization of default reasoning in System (...)
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    Transitive Reasoning with Imprecise Probabilities.Angelo Gilio, Niki Pfeifer & Giuseppe Sanfilippo - 2015 - In S. Destercke & T. Denoeux (eds.), Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2015). Springer LNAI 9161. pp. 95-105.
    We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Finally, we present the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases.
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  7.  49
    Algebraic Aspects and Coherence Conditions for Conjoined and Disjoined Conditionals.Angelo Gilio & Giuseppe Sanfilippo - 2020 - International Journal of Approximate Reasoning 126:98-123.
    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 (...)
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