Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditional Random Quantities and Compounds of Conditionals   In this paper we consider finite conditional random quantities and
conditional previsions assessments in the setting of coherence. We use a
suitable representation for conditional random quantities; in particular the
indicator of a conditional event $E|H$ is looked at as a three-valued quantity
with values 1, or 0, or $p$, where $p$ is the probability of $E|H$. We
introduce a notion of iterated conditional random quantity of the form
$(X|H)|K$ defined as a suitable conditional random quantity, which coincides
with $X|HK$ when $H \subseteq K$. Based on 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.
We examine some cases of logical dependencies, by also showing that the
conjunction may be a conditional event; moreover, we introduce the negation of
the conjunction and by De Morgan's Law the operation of disjunction. Finally,
we give the lower and upper bounds for the conjunction and the disjunction of
two conditional events, by showing that the usual probabilistic properties
continue to hold.

17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas