Search results for " Inference rules"
showing 4 items of 4 documents
Probabilistic entailment and iterated conditionals
2020
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 conditional $(B|K)|(A|H)$, by showing that $A|H$ p-entails $B|K$ if and only if $(B|K)|(A|H) = 1$. Then, we show that a p-consistent family $\mathcal{F}=\{E_1|H_1,E_2|H_2\}$ p-entails a conditional event $E_3|H_3$ if and only if $E_3|H_3=1$, or $(E_3|H_3)|QC(\mathcal{S})=1$ for some nonempty subset $\mathcal{S}$ of $\mathcal{F}$, where $QC(\mathcal{S})$ is the quasi conjunction of the conditional events in $\mathcal{S}$. Then, we examine the inference rules $A…
Logical Operations among Conditional Events: theoretical aspects and applications
2019
We generalize the notions of conjunction and disjunction of two conditional events to the case of $n$ conditional events. These notions are defined, in the setting of coherence, by means of suitable conditional random quantities with values in the interval $[0,1]$. We also define the notion of negation, by verifying De Morgan's Laws. Then, we give some results on coherence of prevision assessments for some families of compounded conditionals and we show that some well known properties which are satisfied by conjunctions and disjunctions of unconditional events are also satisfied by conjunctions and disjunction of conditional events. We also examine in detail the coherence of the prevision a…
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…
Probabilistic inference and syllogisms
2014
Traditionally, syllogisms are arguments with two premises and one conclusion which are constructed by propositions of the form “All S are P ” and “At least one S is P ” and their respective negated versions. We will discuss probabilistic notions of the existential import and the basic sentences type. We will develop an intuitively plausible version of the syllogisms that is able to deal with uncertainty, exceptions and nonmonotonicity. We will develop a new semantics for categorical syllogisms that is based on subjective probability. Specifically, we propose de Finetti’s principle of coherence and its generalization to lower and upper conditional probabilities as the fundamental corner ston…