Paper Info
Title
Iterated Conditionals and Characterization of P-Entailment
Abstract
In this paper we deepen, in the setting of coherence, some results obtained in recent papers on the notion of p-entailment of Adams and its relationship with conjoined and iterated conditionals. We recall that conjoined and iterated conditionals are suitably defined in the framework of conditional random quantities. Given a family F of n conditional events {E-1 vertical bar H-1, ..., E-n vertical bar H-n} we denote by C(F) = (E-1 vertical bar H-1) boolean AND . . . boolean AND (E-n vertical bar H-n) the conjunction of the conditional events in F. We introduce the iterated conditional C(F-2)vertical bar C(F-1), where F-1 and F-2 are two finite families of conditional events, by showing that the prevision of C(F-2) boolean AND C(F-1) is the product of the prevision of C(F-2)vertical bar C(F-1) and the prevision of C(F1). Likewise the well known equality (A boolean AND H)vertical bar H = A vertical bar H, we show that (C(F-2) boolean AND C(F-1))vertical bar C(F-1) = C(F-2)vertical bar C(F-1). Then, we consider the case F-1 = F-2 = F and we verify for the prevision mu of C(F)vertical bar C(F) that the unique coherent assessment is mu = 1 and, as a consequence, C(F)vertical bar C(F) coincides with the constant 1. Finally, by assuming F p-consistent, we deepen some previous characterizations of p-entailment by showing that F p-entails a conditional event En+1 vertical bar Hn+1 if and only if the iterated conditional (En+1 vertical bar Hn+1) vertical bar C(F) is constant and equal to 1. We illustrate this characterization by an example related with weak transitivity.
Year
DOI
Venue
2021
10.1007/978-3-030-86772-0_45
SYMBOLIC AND QUANTITATIVE APPROACHES TO REASONING WITH UNCERTAINTY, ECSQARU 2021
Keywords
DocType
Volume
Coherence, Conditional events, Conditional random quantities, Conditional previsions, Conjoined conditionals, Iterated conditionals, Probabilistic entailment
Conference
12897
ISSN
Citations 
PageRank 
0302-9743
0
0.34
References 
Authors
0
2
Name
Order
Citations
PageRank
Angelo Gilio141942.04
Giuseppe Sanfilippo220417.14