The Consistency Problem for Positive Comprehension Principles

1989 ◽  
Vol 54 (4) ◽  
pp. 1401 ◽  
Author(s):  
M. Forti ◽  
R. Hinnion
Keyword(s):  
Consistency Problem

scholarly journals Formalism and Hilbert’s understanding of consistency problems

2021 ◽  
Author(s):  
Michael Detlefsen
Keyword(s):  
Philosophy Of Mathematics ◽  
Model Construction ◽  
Traditional Model ◽  
Consistency Proof ◽  
Salient Points ◽  
Consistency Problem ◽  
Late Nineteenth ◽  
Similarity And Difference ◽  
Traditional Understanding

AbstractFormalism in the philosophy of mathematics has taken a variety of forms and has been advocated for widely divergent reasons. In Sects. 1 and 2, I briefly introduce the major formalist doctrines of the late nineteenth and early twentieth centuries. These are what I call empirico-semantic formalism (advocated by Heine), game formalism (advocated by Thomae) and instrumental formalism (advocated by Hilbert). After describing these views, I note some basic points of similarity and difference between them. In the remainder of the paper, I turn my attention to Hilbert’s instrumental formalism. My primary aim there will be to develop its formalist elements more fully. These are, in the main, (i) its rejection of the axiom-centric focus of traditional model-construction approaches to consistency problems, (ii) its departure from the traditional understanding of the basic nature of proof and (iii) its distinctively descriptive or observational orientation with regard to the consistency problem for arithmetic. More specifically, I will highlight what I see as the salient points of connection between Hilbert’s formalist attitude and his finitist standard for the consistency proof for arithmetic. I will also note what I see as a significant tension between Hilbert’s observational approach to the consistency problem for arithmetic and his expressed hope that his solution of that problem would dispense with certain epistemological concerns regarding arithmetic once and for all.

The consistency problem for positive comprehension principles

1989 ◽  
Vol 54 (4) ◽  
pp. 1401-1418 ◽  
Author(s):  
M. Forti ◽  
R. Hinnion
Keyword(s):  
Set Theory ◽  
Difficult Problem ◽  
Large Cardinal ◽  
Positive Theory ◽  
Construction Principle ◽  
Short Summary ◽  
Free Construction ◽  
Unpublished Thesis ◽  
Consistency Problem ◽  
Original Construction

Since Gilmore showed that some theory with a positive comprehension scheme is consistent when the axiom of extensionality is dropped and inconsistent with it (see [1] and [2]), the problem of the consistency of various positive comprehension schemes has been investigated. We give here a short classification, which shows clearly the importance of the axiom of extensionality and of the abstraction operator in these consistency problems. The most difficult problem was to show the consistency of the comprehension scheme for positive formulas, with extensionality but without abstraction operator. In his unpublished thesis, Set theory in which the axiom of foundation fails [3], Malitz solved partially this problem but he needed to assume the existence of some unusual kind of large cardinal; as his original construction is very interesting and his thesis is unpublished, we give a short summary of it. M. Forti solved the problem completely by working in ZF with a free-construction principle (sometimes called an anti-foundation axiom), instead of ZF with the axiom of foundation, as Malitz did.This permits one to obtain the consistency of this positive theory, relative to ZF. In his general investigations about “topological set theories” (to be published), E. Weydert has independently proved the same result. The authors are grateful to the Mathematisches Forshungsinstitut Oberwolfach for giving them the opportunity of discussing these subjects and meeting E. Weydert during the meeting “New Foundations”, March 1–7, 1987.

scholarly journals Has the Pandemic Triggered a ‘Paperdemic’? Towards an Assessment of Diagnostic Indicators for COVID-19

2021 ◽  
Author(s):  
AISDL
Keyword(s):  
Predictive Value ◽  
Diagnostic Testing ◽  
Supporting Evidence ◽  
The Novel ◽  
Scientific Publications ◽  
Widespread Belief ◽  
Novel Method ◽  
Consistency Problem ◽  
Novel Coronavirus ◽  
Sensitivity Specificity

This paper is a preliminary step towards the assessment of an alarming widespread belief that victims of the novel coronavirus SARS-CoV-2 include the quality and accuracy of scientific publications about it. Our initial results suggest that this belief cannot be readily ignored, denied, dismissed or refuted, since some genuine supporting evidence can be forwarded for it. This evidence includes an obvious increase in retractions of papers published about the COVID-19 pandemic plus an extra-ordinary phenomenon of inconsistency that we report herein. In fact, we provide a novel method for validating any purported set of the four most prominent indicators of diagnostic testing (Sensitivity, Specificity, Positive Predictive Value, and Negative Predictive Value), by observing that these indicators constitute three rather than four independent quantities. This observation has virtually been unheard of in the open medical literature, and hence researchers have not taken it into consideration. We define two functions, which serve as consistency criteria, since each of them checks consistency for any set of four numerical values (naturally belonging to the interval [0.0,1.0]) claimed to be the four basic diagnostic indicators. Most of the data we came across in various international journals met our criteria for consistency, but in a few cases, there were obvious unexplained blunders. We explored the same consistency problem for some diagnostic data published in 2020 concerning the ongoing COVID-19 pandemic and observed that the afore-mentioned unexplained blunders tended to be on the rise. A systematic extensive statistical assessment of this resumed tendency is warranted.

A Solution for SDN Policy Conflict Consistency Problem

2021 ◽  
pp. 557-565
Author(s):  
Xin-Zhi Tian ◽  
Hai-Jie Shen ◽  
Xiao-Fan Chen ◽  
Cai-Hong Li
Keyword(s):  
Policy Conflict ◽  
Consistency Problem

A Novel Data Consistence Model Based on Virtual Peers in Peer-to-Peer Systems

2020 ◽  
Vol 16 (3) ◽  
pp. 1-16
Author(s):  
Hong He
Keyword(s):  
Data Retrieval ◽  
Peer To Peer ◽  
Data Consistency ◽  
P2p Systems ◽  
Efficient Storage ◽  
Peer To Peer Systems ◽  
Consistency Problem ◽  
Unstructured P2p ◽  
Effectiveness And Efficiency ◽  
P2p System

In recent years, peer-to-peer (P2P) systems have become a promising paradigm to provide efficient storage service in distributed environments. Although its effectiveness has been proven in many areas, the data consistency problem in P2P systems are still an opening issue. This article proposes a novel data consistence model, virtual peers-based data consistency (VPDC), which introduces a set of virtual peers to provide guaranteed data consistency in decentralized and unstructured P2P systems. The VPDC model can be easily implemented in any P2P system without introducing any interference to data retrieval. Theoretical analysis on VPDC is presented to analyze its effectiveness and efficiency, and massive experiments are conducted to evaluate the performance of a VPDC model in a real-world P2P system. The results indicate that it can significantly improve the data consistence of P2P systems and outperform many similar approaches in various experimental settings.

Consistency of Replicated Datasets in Grid Computing

2009 ◽  
pp. 49-58
Author(s):  
Gianni Pucciani ◽  
Flavia Donno ◽  
Andrea Domenici ◽  
Heinz Stockinger
Keyword(s):  
Distributed Systems ◽  
Fault Tolerance ◽  
Grid Computing ◽  
Data Management ◽  
Data Replication ◽  
Data Access ◽  
Grid Middleware ◽  
Pros And Cons ◽  
Consistency Problem ◽  
Replica Consistency

Data replication is a well-known technique used in distributed systems in order to improve fault tolerance and make data access faster. Several copies of a dataset are created and placed at different nodes, so that users can access the replica closest to them, and at the same time the data access load is distributed among the replicas. In today’s Grid middleware solutions, data management services allow users to replicate datasets (i.e., flat files or databases) among storage elements within a Grid, but replicas are often considered read-only because of the absence of mechanisms able to propagate updates and enforce replica consistency. This entry analyzes the replica consistency problem and provides hints for the development of a Replica Consistency Service, highlighting the main issues and pros and cons of several approaches.

scholarly journals Semantic Consistency Checking in Building Ontology from Heterogeneous Sources

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Shihan Yang ◽  
Hongyan Tan ◽  
Jinzhao Wu
Keyword(s):  
Model Checking ◽  
Heterogeneous Data ◽  
Domain Ontology ◽  
Semistructured Data ◽  
Data Sources ◽  
Consistency Checking ◽  
Kripke Structure ◽  
Semantic Consistency ◽  
Heterogeneous Data Sources ◽  
Consistency Problem

Semantic collision is inevitable while building a domain ontology from heterogeneous data sources (semi-)automatically. Therefore, the semantic consistency is indispensable precondition for building a correct ontology. In this paper, a model-checking-based method is proposed to handle the semantic consistency problem with a kind of middle-model methodology, which could extract a domain ontology from structured and semistructured data sources semiautomatically. The method translates the middle model into the Kripke structure, and consistency assertions into CTL formulae, so a consistency checking problem is promoted to a global model checking. Moreover, the feasibility and correctness of the transformation is proved, and case studies are provided.

scholarly journals A Reduction of the NF consistency Problem

2007 ◽  
Vol 72 (1) ◽  
pp. 285-304 ◽  
Author(s):  
Athanassios Tzouvaras
Keyword(s):  
Generic Extension ◽  
Sufficient Condition ◽  
Ground Model ◽  
Necessary And Sufficient Condition ◽  
Coherent Pair ◽  
Consistency Problem ◽  
Coherent Pairs ◽  
Necessary And Sufficient ◽  
Type Shifting

AbstractWe give a necessary and sufficient condition in order that a type-shifting automorphism be constructed on a model of the Theory of Simple Types (TST) by forcing. Namely it is proved that, if for every n ≥ 1 there is a model of TST in the ground model M of ZFC that contains an n-extendible coherent pair, then there is a generic extension M[G] of M that contains a model of TST with a type-shifting automorphism, and hence M[G] contains a model of NF. The converse holds trivially. It is also proved that there exist models of TST containing 1-extendible coherent pairs.

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