Search results for "Disjunction"
showing 10 items of 20 documents
Compound conditionals as random quantities and Boolean algebras
2022
Conditionals play a key role in different areas of logic and probabilistic reasoning, and they have been studied and formalised from different angles. In this paper we focus on the de Finetti's notion of conditional as a three-valued object, with betting-based semantics, and its related approach as random quantity as mainly developed by two of the authors. Compound conditionals have been studied in the literature, but not in full generality. In this paper we provide a natural procedure to explicitly attach conditional random quantities to arbitrary compound conditionals that also allows us to compute their previsions. By studying the properties of these random quantities, we show that, in f…
Micromorphological observations on leaf and pollen ofCapparisL. sect.Capparis(Capparaceae)
2004
Sect. Capparis is represented by a single species, Capparis spinosa L., divided into several intraspecific taxa showing plesiomorphic features and disjunct distributions in the Old World. Leaf surface and pollen features were investigated in the whole group by SEM and light microscope observations. The section is characterized by simple hairs, a reticulate to undulate cuticle, anomocytic stomata surrounded by a peristomal rim, and trizonocolporate, prolate pollen grains. The characteristics of the indumentum appear constant, while the studied taxa are fairly differentiated with respect to cuticular patterns and dimensions of the stomata, and show slight differences in pollen size and exine …
On conditional probabilities and their canonical extensions to Boolean algebras of compound conditionals
2023
In this paper we investigate canonical extensions of conditional probabilities to Boolean algebras of conditionals. Before entering into the probabilistic setting, we first prove that the lattice order relation of every Boolean algebra of conditionals can be characterized in terms of the well-known order relation given by Goodman and Nguyen. Then, as an interesting methodological tool, we show that canonical extensions behave well with respect to conditional subalgebras. As a consequence, we prove that a canonical extension and its original conditional probability agree on basic conditionals. Moreover, we verify that the probability of conjunctions and disjunctions of conditionals in a rece…
Conjunction and Disjunction Among Conditional Events
2017
We generalize, in the setting of coherence, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. Given a prevision assessment on the conjunction of two conditional events, we study the set of coherent extensions for the probabilities of the two conditional events. Then, we introduce by a progressive procedure the notions of conjunction and disjunction for n conditional events. Moreover, by defining the negation of conjunction and of disjunction, we show that De Morgan’s Laws still hold. We also show that the associative and commutative properties are satisfied. Finally, we examine in detail the conjunction for a family \(\mathcal F\) of t…
Conditional Random Quantities and Compounds of Conditionals
2013
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 cohere…
Compound conditionals, Fr\'echet-Hoeffding bounds, and Frank t-norms
2021
Abstract In this paper we consider compound conditionals, Frechet-Hoeffding bounds and the probabilistic interpretation of Frank t-norms. By studying the solvability of suitable linear systems, we show under logical independence the sharpness of the Frechet-Hoeffding bounds for the prevision of conjunctions and disjunctions of n conditional events. In addition, we illustrate some details in the case of three conditional events. We study the set of all coherent prevision assessments on a family containing n conditional events and their conjunction, by verifying that it is convex. We discuss the case where the prevision of conjunctions is assessed by Lukasiewicz t-norms and we give explicit s…
Floristic affinities between the somali and the mediterranean regions
1988
The phytogeographical connections between Somalia and the Mediterranean Region were analyzed. 99 families and about 300 genera turned out to be common to the two areas, representing 67 per cent of the families and 32 per cent of the genera in the whole Somali flora. If considering only the flora of the northern portion of Somalia, these values respectively reach 76 per cent of the families and 40 per cent of the genera. Furthermore several species are common to the two areas, some showing continuous distribution between eastern Africa and the Mediterranean Region, while others have strongly disjunct distribution.
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 Frechet-Hoeffding bounds. Moreover, we study the reverse probabilistic inference from the conjunction $\mathcal…
Quasi conjunction, quasi disjunction, t-norms and t-conorms: Probabilistic aspects
2013
We make a probabilistic analysis related to some inference rules which play an important role in nonmonotonic reasoning. In a coherence-based setting, we study the extensions of a probability assessment defined on $n$ conditional events to their quasi conjunction, and by exploiting duality, to their quasi disjunction. The lower and upper bounds coincide with some well known t-norms and t-conorms: minimum, product, Lukasiewicz, and Hamacher t-norms and their dual t-conorms. On this basis we obtain Quasi And and Quasi Or rules. These are rules for which any finite family of conditional events p-entails the associated quasi conjunction and quasi disjunction. We examine some cases of logical de…
Pseudo-exclusion from paternity due to maternal uniparental disomy 16.
1998
The investigation of a case of disputed paternity revealed indirect exclusion of the alleged father in the haptoglobin system and in the DNA single-locus system D16S309/Hinf I (MS205). The paternity index for the non-exclusion systems was > 10(6). Since both exclusion systems (HP and MS205) are located on chromosome 16, we investigated 10 microsatellite loci covering this chromosome with 10-20 cM resolution. Analysis of the child's chromosome showed only alleles of maternal origin and lack of inheritance of paternal alleles for five informative loci. The markers close to the centromere of chromosome 16 were heterozygous, whereas distal loci were either heterozygous or homozygous for materna…