Related papers: Probabilistic inferences from conjoined to iterate…
We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability…
In this paper we exploit the notions of conjoined and iterated conditionals, which are defined in the setting of coherence by means of suitable conditional random quantities with values in the interval $[0,1]$. We examine the iterated…
It is well know that basic conditionals satisfy some desirable basic logical and probabilistic properties, such as the compound probability theorem, but checking the validity of these becomes trickier when we switch to compound and iterated…
In this paper we recall some results for conditional events, compound conditionals, conditional random quantities, p-consistency, and p-entailment. Then, we show the equivalence between bets on conditionals and conditional bets, by…
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…
Conditionals play a key role in different areas of logic and probabilistic reasoning, and they have been studied and formalized from different angles. In this paper we focus on the de Finetti's notion of conditional as a three-valued…
An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation…
The main result presented in this article is that probability can fundamentally be characterized as a subset of conditional expectation induced by a plausible preorder on random quantities. This is justified by the fact that probability is…
The language of probability is used to define several different types of conditional statements. There are four principal types: subjunctive, material, existential, and feasibility. Two further types of conditionals are defined using the…
While a large body of work has scrutinized the meaning of conditional sentences, considerably less attention has been paid to formal models of their pragmatic use and interpretation. Here, we take a probabilistic approach to pragmatic…
This paper develops a trivalent semantics for the truth conditions and the probability of the natural language indicative conditional. Our framework rests on trivalent truth conditions first proposed by W. Cooper and yields two logics of…
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…
In this talk - based on the results of a forthcoming paper (Coletti, Scozzafava and Vantaggi 2002), presented also by one of us at the Conference on "Non Classical Logic, Approximate Reasoning and Soft-Computing" (Anacapri, Italy, 2001) -…
We consider the problem of defining conditional objects (a|b), which would allow one to regard the conditional probability Pr(a|b) as a probability of a well-defined event rather than as a shorthand for Pr(ab)/Pr(b). The next issue is to…
The definition of the conditional probability is very important in the theory of the probability. This definition is based on the fact, that random events can be simultaneously measurable. This paper deal with the problem of conditioning…
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…
We present probabilistic approaches to check the validity of selected connexive principles within the setting of coherence. Connexive logics emerged from the intuition that conditionals of the form "If $\sim A$, then $A$", should not hold,…
In this work we first illustrate the subjective theory of de Finetti. We recall the notion of coherence for both the betting scheme and the penalty criterion, by considering the unconditional and conditional cases. We show the equivalence…
Modus ponens (\emph{from $A$ and "if $A$ then $C$" infer $C$}, short: MP) is one of the most basic inference rules. The probabilistic MP allows for managing uncertainty by transmitting assigned uncertainties from the premises to the…
We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A…