scholarly journals Admissibility in Probabilistic Argumentation

2021 ◽  
Author(s):  
Christel Baier ◽  
Martin Diller ◽  
Clemens Dubslaff ◽  
Sarah Alice Gaggl ◽  
Holger Hermanns ◽  
...  
Keyword(s):  
Joint Probability ◽  
Building Blocks ◽  
Joint Probability Distribution ◽  
Proof Of Concept ◽  
Abstract Argumentation ◽  
Classical Setting ◽  
Probabilistic Setting ◽  
Probabilistic Argumentation ◽  
Conservative Extensions ◽  
Quantitative Treatment

Abstract argumentation is a prominent reasoning framework. It comes with a variety of semantics, and has lately been enhanced by probabilities to enable a quantitative treatment of argumentation. While admissibility is a fundamental notion in the classical setting, it has been merely reflected so far in the probabilistic setting. In this paper, we address the quantitative treatment of argumentation based on probabilistic notions of admissibility in a way that they form fully conservative extensions of classical notions. In particular, our building blocks are not the beliefs regarding single arguments. Instead we start from the fairly natural idea that whatever argumentation semantics is to be considered, semantics systematically induces constraints on the joint probability distribution on the sets of arguments. In some cases there might be many such distributions, even infinitely many ones, in other cases there may be one or none. Standard semantic notions are shown to induce such sets of constraints, and so do their probabilistic extensions. This allows them to be tackled by SMT solvers, as we demonstrate by a proof-of-concept implementation. We present a taxonomy of semantic notions, also in relation to published work, together with a running example illustrating our achievements.

scholarly journals Probability elicitation using geostatistics in hydrocarbon exploration

2021 ◽  
Author(s):  
André Luís Morosov ◽  
Reidar Brumer Bratvold
Keyword(s):  
Value Creation ◽  
Decision Process ◽  
Conceptual Models ◽  
Joint Probability ◽  
Decision Makers ◽  
Hydrocarbon Exploration ◽  
Joint Probability Distribution ◽  
Proof Of Concept ◽  
Geological Information ◽  
Decision Supporting

AbstractThe exploratory phase of a hydrocarbon field is a period when decision-supporting information is scarce while the drilling stakes are high. Each new prospect drilled brings more knowledge about the area and might reveal reserves, hence choosing such prospect is essential for value creation. Drilling decisions must be made under uncertainty as the available geological information is limited and probability elicitation from geoscience experts is key in this process. This work proposes a novel use of geostatistics to help experts elicit geological probabilities more objectively, especially useful during the exploratory phase. The approach is simpler, more consistent with geologic knowledge, more comfortable for geoscientists to use and, more comprehensive for decision-makers to follow when compared to traditional methods. It is also flexible by working with any amount and type of information available. The workflow takes as input conceptual models describing the geology and uses geostatistics to generate spatial variability of geological properties in the vicinity of potential drilling prospects. The output is stochastic realizations which are processed into a joint probability distribution (JPD) containing all conditional probabilities of the process. Input models are interactively changed until the JPD satisfactory represents the expert’s beliefs. A 2D, yet realistic, implementation of the workflow is used as a proof of concept, demonstrating that even simple modeling might suffice for decision-making support. Derivative versions of the JPD are created and their effect on the decision process of selecting the drilling sequence is assessed. The findings from the method application suggest ways to define the input parameters by observing how they affect the JPD and the decision process.

scholarly journals A TWO-CLASS RETRIAL SYSTEM WITH COUPLED ORBIT QUEUES

2017 ◽  
Vol 31 (2) ◽  
pp. 139-179 ◽  
Author(s):  
Ioannis Dimitriou
Keyword(s):  
Performance Metrics ◽  
Kernel Method ◽  
Length Distribution ◽  
Probability Generating Function ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Single Server ◽  
Method Performance ◽  
Service Station ◽  
Queue Length Distribution

We consider a single server system accepting two types of retrial customers, which arrive according to two independent Poisson streams. The service station can handle at most one customer, and in case of blocking, typeicustomer,i=1, 2, is routed to a separate typeiorbit queue of infinite capacity. Customers from the orbits try to access the server according to the constant retrial policy. We consider coupled orbit queues, and thus, when both orbit queues are non-empty, the orbit queueitries to re-dispatch a blocked customer of typeito the main service station after an exponentially distributed time with rate μi. If an orbit queue empties, the other orbit queue changes its re-dispatch rate from μito$\mu_{i}^{\ast}$. We consider both exponential and arbitrary distributed service requirements, and show that the probability generating function of the joint stationary orbit queue length distribution can be determined using the theory of Riemann (–Hilbert) boundary value problems. For exponential service requirements, we also investigate the exact tail asymptotic behavior of the stationary joint probability distribution of the two orbits with either an idle or a busy server by using the kernel method. Performance metrics are obtained, computational issues are discussed and a simple numerical example is presented.

scholarly journals Reducing the Complexity of Casual Representation in Bayesian Belief Network

F1000Research ◽  
2021 ◽  
Vol 10 ◽  
pp. 1243
Author(s):  
Yit Yin Wee ◽  
Shing Chiang Tan ◽  
KuokKwee Wee
Keyword(s):  
Causal Model ◽  
Knowledge Engineering ◽  
Joint Probability ◽  
Bayesian Belief Network ◽  
Joint Probability Distribution ◽  
Causal Knowledge ◽  
Belief Network ◽  
Track Record ◽  
Probability Table ◽  
Causal Framework

Background: Bayesian Belief Network (BBN) is a well-established causal framework that is widely adopted in various domains and has a proven track record of success in research and application areas. However, BBN has weaknesses in causal knowledge elicitation and representation. The representation of the joint probability distribution in the Conditional Probability Table (CPT) has increased the complexity and difficulty for the user either in comprehending the causal knowledge or using it as a front-end modelling tool.   Methods: This study aims to propose a simplified version of the BBN ─ Bayesian causal model, which can represent the BBN intuitively and proposes an inference method based on the simplified version of BBN. The CPT in the BBN is replaced with the causal weight in the range of[-1,+1] to indicate the causal influence between the nodes. In addition, an inferential algorithm is proposed to compute and propagate the influence in the causal model.  Results: A case study is used to validate the proposed inferential algorithm. The results show that a Bayesian causal model is able to predict and diagnose the increment and decrement as in BBN.   Conclusions: The Bayesian causal model that serves as a simplified version of BBN has shown its advantages in modelling and representation, especially from the knowledge engineering perspective.

scholarly journals Site-Selective [2+2+n] Cycloadditions for Rapid, Scalable Access to Alkynylated Polycyclic Aromatic Hydrocarbons

2019 ◽  
Author(s):  
Gavin R. Kiel ◽  
Harrison Bergman ◽  
T. Don Tilley
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Aromatic Hydrocarbons ◽  
Structural Complexity ◽  
Building Blocks ◽  
Synthetic Methods ◽  
Proof Of Concept ◽  
Site Selectivity ◽  
Polycyclic Aromatic ◽  
Site Selective ◽  
Nanometer Regime

Polycyclic aromatic hydrocarbons (PAHs) are attractive synthetic building blocks for more complex conjugated nanocarbons, but their use for this purpose requires appreciable quantities of a PAH with reactive functional groups. Despite tremendous recent advances, most synthetic methods cannot satisfy these demands. Here we present a general and scalable [2+2+n] (n = 1 or 2) cycloaddition strategy to access PAHs that are decorated with synthetically versatile alkynyl groups and its application to seven structurally diverse PAH ring systems (thirteen new alkynylated PAHs in total). The critical discovery is the site-selectivity of an Ir-catalyzed [2+2+2] cycloaddition, which preferentially cyclizes tethered diyne units with preservation of other (peripheral) alkynyl groups. The potential for generalization of the site-selectivity to other [2+2+n] reactions is demonstrated by identification of a Cp<sub>2</sub>Zr-mediated [2+2+1] / metallacycle transfer sequence for synthesis of an alkynylated, selenophene-annulated PAH. The new PAHs are excellent synthons for macrocyclic conjugated nanocarbons. As a proof of concept, four were subjected to Mo catalysis to afford large, PAH-containing arylene ethylene macrocycles, which possess a range of cavity sizes reaching well into the nanometer regime. More generally, this work is a demonstration of how site-selective reactions can be harnessed to rapidly build up structural complexity in a practical, scalable fashion.

scholarly journals Perishable Inventory System with Postponed Demands and Negative Customers

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Paul Manuel ◽  
B. Sivakumar ◽  
G. Arivarignan
Keyword(s):  
Steady State ◽  
Joint Probability ◽  
Inventory System ◽  
Arrival Process ◽  
Inventory Level ◽  
Joint Probability Distribution ◽  
Time Interval ◽  
Negative Customers ◽  
Perishable Inventory System ◽  
Number Of Customers

This article considers a continuous review perishable (s,S) inventory system in which the demands arrive according to a Markovian arrival process (MAP). The lifetime of items in the stock and the lead time of reorder are assumed to be independently distributed as exponential. Demands that occur during the stock-out periods either enter a pool which has capacity N(<∞) or are lost. Any demand that takes place when the pool is full and the inventory level is zero is assumed to be lost. The demands in the pool are selected one by one, if the replenished stock is above s, with time interval between any two successive selections distributed as exponential with parameter depending on the number of customers in the pool. The waiting demands in the pool independently may renege the system after an exponentially distributed amount of time. In addition to the regular demands, a second flow of negative demands following MAP is also considered which will remove one of the demands waiting in the pool. The joint probability distribution of the number of customers in the pool and the inventory level is obtained in the steady state case. The measures of system performance in the steady state are calculated and the total expected cost per unit time is also considered. The results are illustrated numerically.

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