Search results for " Disjunction"
showing 4 items of 14 documents
Generalized Logical Operations among Conditional Events
2018
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 we examine the Fr'echet-Hoeffding bounds. Moreover, we study the reverse probabilistic inference from the conjunction $mathc…
Compounds of conditionals and iterated conditioning under coherence
2017
We discuss the problem of defining logical operations among conditional events. Differently from many authors, we define the conjunction and disjunction in the setting of conditional random quantities. In probability theory and in probability logic a relevant problem, largely discussed by many authors, is that of defining logical operations among conditional events. In the many works concerning these operations, the conjunction and disjunction have been usually defined as suitable conditional events. In Kaufmann 2009 it has been proposed a theory for the compounds of conditionals which has been framed in the setting of coherence in (Gilio and Sanfilippo , 2013, 2014) In this framework, whic…
On compound and iterated conditionals
2021
We illustrate the notions of compound and iterated conditionals introduced, in recent papers, as suitable conditional random quantities, in the framework of coherence. We motivate our definitions by examining some concrete examples. Our logical operations among conditional events satisfy the basic probabilistic properties valid for unconditional events. We show that some, intuitively acceptable, compound sentences on conditionals can be analyzed in a rigorous way in terms of suitable iterated conditionals. We discuss the Import-Export principle, which is not valid in our approach, by also examining the inference from a material conditional to the associated conditional event. Then, we illus…
Conjunction, Disjunction and Iterated Conditioning of Conditional Events
2013
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 lower and upper bounds on the conjunction. We also examine an apparent paradox concerning stochastic independence which can actually be explained in terms of uncorrelation. We briefly introduce the…