Logics preserving degrees of truth from varieties of residuated lattices

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Logics preserving degrees of truth from varieties of residuated lattices"

Transcription

1 Corrigendum Logics preserving degrees of truth from varieties of residuated attices FÉLIX BOU and FRANCESC ESTEVA, Artificia Inteigence Research Institute IIIA - CSIC), Beaterra, Spain. E-mai: JOSEP MARIA FONT, Department of Probabiity, Logic and Statistics, Facuty of Mathematics, University of Barceona, Spain. E-mai: ÀNGEL J. GIL, Departament d Economia i Empresa, Universitat Pompeu Fabra, Barceona, Spain. E-mai: LLUÍS GODO, Artificia Inteigence Research Institute IIIA - CSIC), Beaterra, Spain. E-mai: ANTONI TORRENS and VENTURA VERDÚ, Department of Probabiity, Logic and Statistics, Facuty of Mathematics, University of Barceona, Spain. E-mai: J Logic Computation December 2009; 19: ; doi: /ogcom/exp030 Logics preserving degrees of truth from varieties of residuated attices FÉLIX BOU and JOSEP MARIA FONT, Department of Probabiity, Logic and Statistics, Facuty of Mathematics, University of Barceona. E-mai: Abstract A wrong argument in the proof of one of the main resuts in the paper is corrected. The resut itsef remains true. The right proof incorporates the basic ideas in the originay aeged proof, but in a more restricted construction. eywords: substructura ogic, many-vaued ogic, degrees of truth, residuated attices, protoagebraic ogic. Vo. 22 No. 3, The Author, Pubished by Oxford University Press. A rights reserved. For Permissions, pease emai: Pubished onine March 1, 2011 doi: /ogcom/exr003

2 662 Corrigendum The proof of the ast impication in Theorem 4.4 of the referenced paper [1] is wrong. At a certain point, it performs a construction on an arbitrary agebra but the properties used in its deveopment impicity assume that the agebra is in fact a residuated attice, which it needs not be. Here, we present a correct proof done by working ony in the formua agebra, foowing the same ideas and performing essentiay the same construction, moduo a certain crucia emma that characterizes the supremum operation in the attice of theories of one of the ogics considered in [1]. Let us reca the necessary background. Let be an arbitrary variety of commutative, integra residuated attices. The paper [1] studies two finitary ogics associated with each such, which are denoted by their consequence reations: The first one, denoted by,isthetruth-preserving ogic determined by the agebras in when their maximum 1 which is aso the unit of the monoid structure of the fusion operation ) is taken as representing truth; the second one, denoted by =,istheogic preserving degrees of truth determined by the ordering reation of the agebras in which are aways attices). More precisey, for any n 1 and any formuas ψ,ϕ 0,...,ϕ n 1 : ψ A, v HomFm,A), vψ)=1. ϕ 0,...,ϕ n 1 ψ A, v HomFm,A), if vϕ i )=1 for a i <n, then vψ)=1. = ψ A, v HomFm,A), vψ)=1. ϕ 0,...,ϕ n 1 = ψ A, v HomFm,A), a A, if vϕ i ) a for a i <n, then vψ) a. The formua agebra is denoted by Fm, and its universe i.e. the set of a formuas) by Fm. The paper [1] focuses on the ess-known ogic =. The ogic is the one customariy associated with, and has been extensivey studied, see [3]; in particuar, it is finitey and reguary agebraizabe, having as its argest equivaent agebraic semantics. The properties needed here that aready appear in [1] are summarized beow. 1) The two ogics have the same theorems, and the ogic is an extension of the ogic = by either of the foowing rues: Modus Ponens for α,α β β); Adjunction for α,β α β); or Squaring α α 2 ); the exponentia notation denotes iteration of the operation. Hence, every theory of is in particuar a theory of =. 2) For a α,β Fm, α β = α β α = β. The second expression means that A, v HomFm,A), vα) vβ). 3) The ogic satisfies the Loca Deduction-Detachment Theorem: For a Γ {α,β} Fm,Γ,α β if and ony if there is some n ω such that Γ α n β. 4) The Leibniz congruence Ω T of a theory T of is defined from T with the hep of the equivaence connective as foows: for any α,β Fm, α,β Ω T α β T. 5) For any theory T of = there is a theory T + of such that T + T and Ω T + =Ω T. Moreover, we need the foowing properties, not expicity mentioned in [1]: 6) For a α Fm, α 1) α and 1 α) α. Reca that 1 is a constant term which is a theorem of both ogics. 7) For a α 1,...,α n Fm,α 1 α n α i for each i {1,...,n}.

3 8) For a α 1,...,α n Fm and a k, α k 1 α k n) α1 α n ) k. 9) For a α,β Fm,if α β then α k β k for a k. 10) For a α,α,β,β Fm,if α β and α β, then α α ) β β ). 11) For a α,β Fm, α β) β α). 12) For a α,β Fm, α β β α) ). Corrigendum 663 A these properties are easiy shown using the first equivaence in 2) and the corresponding properties of the ordering reation and the operations and in commutative, integra residuated attices; for instance, 10) foows from the monotonicity of with respect to order, 11) corresponds to its commutative character, and so on. Lemma. Let S and T be two theories of. Then, the smaest theory of which contains S T is the set { ϕ Fm: γ S, δ T such that γ δ) ϕ }. Proof. Let us denote the dispayed set by L. That this set contains both S and T is a consequence of 6). In order to show that L is cosed under the rues of, et us assume that ϕ 1,...,ϕ n ϕ and that ϕ 1,...,ϕ n L; we have to prove that ϕ L. Using 7) one can see that the assumption impies that ϕ 1 ϕ n ϕ. Now, by 3), there is some ω such that ϕ 1... ϕ n ) ϕ, and by 8) this impies that ϕ 1 ϕ n) ϕ. Since for every i {1,...,n},ϕ i L, there are formuas γ i S and δ i T such that γ i δ i ) ϕ i. Using 9), 8), 10) and 11) in succession we obtain γ 1... γ n δ 1... δ n) ϕ 1... ϕ n). We have aready seen that ϕ1... ϕ n ) ϕ, therefore γ 1... γ n δ 1... δ n) ϕ. By one of the properties in 1), the theories of are cosed under fusion, hence γ1... γ n S and δ1... δ n T. Thus, by definition, ϕ L. This shows that L is a theory of. Finay, L is the smaest such theory containing S T:IfT is a theory of such that S T T, and ϕ L, by definition there are γ S and δ T such that γ δ) ϕ. These facts impy that γ,δ T and aso that γ δ) ϕ T. Since by 1) the theories of are cosed under fusion and Modus Ponens, we obtain first that γ δ T, and then that ϕ T. This coses the proof. Observe that, by 2), the property that γ δ) ϕ can be equivaenty stated as γ δ = ϕ,so that, even if it is written using, it tes us something about the theories of =. It is in this form that it wi be used in a crucia step in the next proof. We can now give the right proof that corrects the origina one in [1]. This proof uses some standard facts on agebraizabiity and protoagebraicity that can be found in [2]. Theorem 4.4 of [1]. Let be a variety of residuated attices. Then the foowing conditions are equivaent: 1. The ogic = is protoagebraic.

4 664 Corrigendum 2. For a A and a F Fi = A), F + =max{s Fi A):G F}. 3. A matrix A,F is a reduced mode of = if and ony if A and F is a attice fiter of A such that {1} is the ony impicative fiter of A contained in F. 4. For every A and every F,G Fi = A), if G F and Ω A F =Id then Ω A G=Id. Proof of 4 1. We are going to show that the Leibniz operator Ω is monotonic over the theories of = ; Theorem of [2] guarantees that this amounts to = being protoagebraic. Let Fm be the formua agebra and et S,T be two theories of = with S T; we have to prove that Ω S Ω T. It is easy to see that, using 5), we can repace S with S + to the same effect; therefore, it wi be simper to assume, without oss of generaity, that S is a theory of. Now, using 5) again, we can consider the theory T + of associated with T, and denote by L the smaest theory of that contains S T +. Caim: T + L T. Proof of the caim. It is cear that T + L, so we have to prove that L T. Using the previous Lemma, it is enough to prove that if γ S, δ T + and γ δ) ϕ, then ϕ T. Since T + is a theory of, by 12) and Modus Ponens it foows that γ γ δ) T +. Now by 4) this tes us that γ,γ δ Ω T + =Ω T. But γ S T, so by the compatibiity of Ω T with T we get that γ δ T. Finay, by 2), the assumption that γ δ) ϕ can be equivaenty stated as γ δ = ϕ, and this aows us to concude that ϕ T. This competes the proof of the caim. By agebraizabiity of, the Leibniz operator Ω is monotonic over its theories. Since both T + and L are theories of, from the caim it foows that Ω T =Ω T + Ω L; hence, Ω T + is compatibe with L, and it is aso compatibe with T by definition; so, it makes sense to factor out L and T by Ω T + and we wi obtain fiters of the respective ogics on the quotient agebra. Put A:=Fm/Ω T +, L :=L/Ω T + and T :=T/Ω T +. Then L is a fiter of and hence by 1) a fiter of =, whie T is a fiter of = ; thus, L, T Fi = A), and by the caim, L T. Since is the argest equivaent agebraic semantics of, we know that A. And since Ω T =Ω T + we know that Ω A T =Ω T/Ω T + =Id. Thus, a the conditions required in item 4 of the present theorem are satisfied, and the assumption impies that Ω A L =Id. But since Ω A L =Ω L/Ω T +, it foows that Ω T + =Ω L. Agebraizabiity of impies that Ω is one-to-one over its theories, therefore T + =L, which is the same as S T +. Since both are theories of, we can use monotonicity again and obtain that Ω S Ω T + =Ω T. This competes the proof that Ω is monotonic over the theories of =. Funding Spanish Ministerio de Ciencia e Innovación TIN C04-01 to F.B.); EU Eurocores FP006/FFI E/FILO to F.B.); Spanish Ministerio de Ciencia e Innovación MTM to J.M.F.); Cataan Departament d Innovació, Universitats i Empresa 2009SGR-1433 to F.B. and J.M.F.). References [1] F. Bou, F. Esteva, J. M. Font, A. Gi, L. Godo, A. Torrens, and V. Verdú. Logics preserving degrees of truth from varieties of residuated attices. Journa of Logic and Computation, 19, , 2009.

5 Corrigendum 665 [2] J. Czeakowski. Protoagebraic ogics, Vo. 10 of Trends in Logic - Studia Logica Library. uwer Academic Pubishers, [3] N. Gaatos, P. Jipsen, T. owaski, and H. Ono. Residuated attices: an agebraic gimpse at substructura ogics, Vo. 151 of Studies in Logic and the Foundations of Mathematics. Esevier, 2007.

ASYMPTOTIC DIRECTION FOR RANDOM WALKS IN RANDOM ENVIRONMENTS arxiv:math/0512388v2 [math.pr] 11 Dec 2007

ASYMPTOTIC DIRECTION FOR RANDOM WALKS IN RANDOM ENVIRONMENTS arxiv:math/0512388v2 [math.pr] 11 Dec 2007 ASYMPTOTIC DIRECTION FOR RANDOM WALKS IN RANDOM ENVIRONMENTS arxiv:math/0512388v2 [math.pr] 11 Dec 2007 FRANÇOIS SIMENHAUS Université Paris 7, Mathématiques, case 7012, 2, pace Jussieu, 75251 Paris, France

More information

DEGREES OF ORDERS ON TORSION-FREE ABELIAN GROUPS

DEGREES OF ORDERS ON TORSION-FREE ABELIAN GROUPS DEGREES OF ORDERS ON TORSION-FREE ABELIAN GROUPS ASHER M. KACH, KAREN LANGE, AND REED SOLOMON Abstract. We show that if H is an effectivey competey decomposabe computabe torsion-free abeian group, then

More information

DEGREES OF ORDERS ON TORSION-FREE ABELIAN GROUPS

DEGREES OF ORDERS ON TORSION-FREE ABELIAN GROUPS 1 DEGREES OF ORDERS ON TORSION-FREE ABELIAN GROUPS 2 ASHER M. KACH, KAREN LANGE, AND REED SOLOMON Abstract. We show that if H is an effectivey competey decomposabe computabe torsion-free abeian group,

More information

Section 3 Sequences and Limits, Continued.

Section 3 Sequences and Limits, Continued. Section 3 Sequences and Limits, Continued. Lemma 3.6 Let {a n } n N be a convergent sequence for which a n 0 for all n N and it α 0. Then there exists N N such that for all n N. α a n 3 α In particular

More information

Hybrid Process Algebra

Hybrid Process Algebra Hybrid Process Agebra P.J.L. Cuijpers M.A. Reniers Eindhoven University of Technoogy (TU/e) Den Doech 2 5600 MB Eindhoven, The Netherands Abstract We deveop an agebraic theory, caed hybrid process agebra

More information

With the arrival of Java 2 Micro Edition (J2ME) and its industry

With the arrival of Java 2 Micro Edition (J2ME) and its industry Knowedge-based Autonomous Agents for Pervasive Computing Using AgentLight Fernando L. Koch and John-Jues C. Meyer Utrecht University Project AgentLight is a mutiagent system-buiding framework targeting

More information

Betting Strategies, Market Selection, and the Wisdom of Crowds

Betting Strategies, Market Selection, and the Wisdom of Crowds Betting Strategies, Market Seection, and the Wisdom of Crowds Wiemien Kets Northwestern University w-kets@keogg.northwestern.edu David M. Pennock Microsoft Research New York City dpennock@microsoft.com

More information

Life Contingencies Study Note for CAS Exam S. Tom Struppeck

Life Contingencies Study Note for CAS Exam S. Tom Struppeck Life Contingencies Study Note for CAS Eam S Tom Struppeck (Revised 9/19/2015) Introduction Life contingencies is a term used to describe surviva modes for human ives and resuting cash fows that start or

More information

Irish Life Tables No. 14

Irish Life Tables No. 14 3 June 004 Life epectancy at birth Irish Life Tabes No. 14 001-003 Life epectancy 85 80 75 70 65 60 55 Maes Femaes Life epectancy at birth Area Maes Femaes Ireand 75.1 80.3 EU 15 75.8 81.6 EU 5 74.8 81.1

More information

Two Dimensional YD-modules over U q (sl 2 ) are trivial

Two Dimensional YD-modules over U q (sl 2 ) are trivial Two Dimensiona YD-modues over U q (s 2 ) are trivia Emine Yidirim University of New Brunswick June 27th, 2014 Emine Yidirim (University of New Brunswick) Hopf Agebras in (co)action June 27th, 2014 1 /

More information

SELECTING THE SUITABLE ERP SYSTEM: A FUZZY AHP APPROACH. Ufuk Cebeci

SELECTING THE SUITABLE ERP SYSTEM: A FUZZY AHP APPROACH. Ufuk Cebeci SELECTING THE SUITABLE ERP SYSTEM: A FUZZY AHP APPROACH Ufuk Cebeci Department of Industria Engineering, Istanbu Technica University, Macka, Istanbu, Turkey - ufuk_cebeci@yahoo.com Abstract An Enterprise

More information

Risk Margin for a Non-Life Insurance Run-Off

Risk Margin for a Non-Life Insurance Run-Off Risk Margin for a Non-Life Insurance Run-Off Mario V. Wüthrich, Pau Embrechts, Andreas Tsanakas February 2, 2011 Abstract For sovency purposes insurance companies need to cacuate so-caed best-estimate

More information

ELECTRONIC FUND TRANSFERS YOUR RIGHTS AND RESPONSIBILITIES

ELECTRONIC FUND TRANSFERS YOUR RIGHTS AND RESPONSIBILITIES About ELECTRONIC FUND TRANSFERS YOUR RIGHTS AND RESPONSIBILITIES The Eectronic Fund Transfers we are capabe of handing for consumers are indicated beow, some of which may not appy your account. Some of

More information

NCH Software MoneyLine

NCH Software MoneyLine NCH Software MoneyLine This user guide has been created for use with MoneyLine Version 2.xx NCH Software Technica Support If you have difficuties using MoneyLine pease read the appicabe topic before requesting

More information

Secure Network Coding with a Cost Criterion

Secure Network Coding with a Cost Criterion Secure Network Coding with a Cost Criterion Jianong Tan, Murie Médard Laboratory for Information and Decision Systems Massachusetts Institute of Technoogy Cambridge, MA 0239, USA E-mai: {jianong, medard}@mit.edu

More information

On Capacity Scaling in Arbitrary Wireless Networks

On Capacity Scaling in Arbitrary Wireless Networks On Capacity Scaing in Arbitrary Wireess Networks Urs Niesen, Piyush Gupta, and Devavrat Shah 1 Abstract arxiv:07112745v3 [csit] 3 Aug 2009 In recent work, Özgür, Lévêque, and Tse 2007) obtained a compete

More information

Chapter 3: JavaScript in Action Page 1 of 10. How to practice reading and writing JavaScript on a Web page

Chapter 3: JavaScript in Action Page 1 of 10. How to practice reading and writing JavaScript on a Web page Chapter 3: JavaScript in Action Page 1 of 10 Chapter 3: JavaScript in Action In this chapter, you get your first opportunity to write JavaScript! This chapter introduces you to JavaScript propery. In addition,

More information

Imaginary quadratic orders with given prime factor of class number

Imaginary quadratic orders with given prime factor of class number Imaginary quadratic orders with given rime factor of cass number Aexander Rostovtsev, St. Petersburg State Poytechnic University, rostovtsev@ss.stu.neva.ru Abstract Abeian cass grou C(D) of imaginary quadratic

More information

Key Features of Life Insurance

Key Features of Life Insurance Key Features of Life Insurance Life Insurance Key Features The Financia Conduct Authority is a financia services reguator. It requires us, Aviva, to give you this important information to hep you to decide

More information

Uncertain Bequest Needs and Long-Term Insurance Contracts 1

Uncertain Bequest Needs and Long-Term Insurance Contracts 1 Uncertain Bequest Needs and Long-Term Insurance Contracts 1 Wenan Fei (Hartford Life Insurance) Caude Fuet (Université du Québec à Montréa and CIRPEE) Harris Schesinger (University of Aabama) Apri 22,

More information

α α λ α = = λ λ α ψ = = α α α λ λ ψ α = + β = > θ θ β > β β θ θ θ β θ β γ θ β = γ θ > β > γ θ β γ = θ β = θ β = θ β = β θ = β β θ = = = β β θ = + α α α α α = = λ λ λ λ λ λ λ = λ λ α α α α λ ψ + α =

More information

Distributed Strategic Interleaving with Load Balancing

Distributed Strategic Interleaving with Load Balancing Distributed Strategic Intereaving with Load Baancing J.A. Bergstra 1,2 and C.A. Middeburg 1,3 1 Programming Research Group, University of Amsterdam, P.O. Box 41882, 1009 DB Amsterdam, the Netherands 2

More information

Remarks on Non-Fregean Logic

Remarks on Non-Fregean Logic STUDIES IN LOGIC, GRAMMAR AND RHETORIC 10 (23) 2007 Remarks on Non-Fregean Logic Mieczys law Omy la Institute of Philosophy University of Warsaw Poland m.omyla@uw.edu.pl 1 Introduction In 1966 famous Polish

More information

c S. Burris and H.P. Sankappanavar All Rights Reserved ISBN 978-0-9880552-0-9

c S. Burris and H.P. Sankappanavar All Rights Reserved ISBN 978-0-9880552-0-9 ii c S. Burris and H.P. Sankappanavar A Rights Reserved ISBN 978-0-9880552-0-9 The authors permit this PDF fie of our book to be freey copied, distributed and printed, for non-commercia educationa purposes,

More information

NCH Software Express Accounts Accounting Software

NCH Software Express Accounts Accounting Software NCH Software Express Accounts Accounting Software This user guide has been created for use with Express Accounts Accounting Software Version 5.xx NCH Software Technica Support If you have difficuties using

More information

Early access to FAS payments for members in poor health

Early access to FAS payments for members in poor health Financia Assistance Scheme Eary access to FAS payments for members in poor heath Pension Protection Fund Protecting Peope s Futures The Financia Assistance Scheme is administered by the Pension Protection

More information

Capacity of Multi-service Cellular Networks with Transmission-Rate Control: A Queueing Analysis

Capacity of Multi-service Cellular Networks with Transmission-Rate Control: A Queueing Analysis Capacity of Muti-service Ceuar Networs with Transmission-Rate Contro: A Queueing Anaysis Eitan Atman INRIA, BP93, 2004 Route des Lucioes, 06902 Sophia-Antipois, France aso CESIMO, Facutad de Ingeniería,

More information

NCH Software FlexiServer

NCH Software FlexiServer NCH Software FexiServer This user guide has been created for use with FexiServer Version 1.xx NCH Software Technica Support If you have difficuties using FexiServer pease read the appicabe topic before

More information

Betting on the Real Line

Betting on the Real Line Betting on the Rea Line Xi Gao 1, Yiing Chen 1,, and David M. Pennock 2 1 Harvard University, {xagao,yiing}@eecs.harvard.edu 2 Yahoo! Research, pennockd@yahoo-inc.com Abstract. We study the probem of designing

More information

Risk Margin for a Non-Life Insurance Run-Off

Risk Margin for a Non-Life Insurance Run-Off Risk Margin for a Non-Life Insurance Run-Off Mario V. Wüthrich, Pau Embrechts, Andreas Tsanakas August 15, 2011 Abstract For sovency purposes insurance companies need to cacuate so-caed best-estimate reserves

More information

A short guide to making a medical negligence claim

A short guide to making a medical negligence claim A short guide to making a medica negigence caim Introduction Suffering from an incident of medica negigence is traumatic and can have a serious ong-term impact on both the physica and menta heath of affected

More information

Fast Robust Hashing. ) [7] will be re-mapped (and therefore discarded), due to the load-balancing property of hashing.

Fast Robust Hashing. ) [7] will be re-mapped (and therefore discarded), due to the load-balancing property of hashing. Fast Robust Hashing Manue Urueña, David Larrabeiti and Pabo Serrano Universidad Caros III de Madrid E-89 Leganés (Madrid), Spain Emai: {muruenya,darra,pabo}@it.uc3m.es Abstract As statefu fow-aware services

More information

Online Supplement for The Robust Network Loading Problem under Hose Demand Uncertainty: Formulation, Polyhedral Analysis, and Computations

Online Supplement for The Robust Network Loading Problem under Hose Demand Uncertainty: Formulation, Polyhedral Analysis, and Computations Onine Suppement for The Robust Network Loading Probem under Hose Demand Uncertaint: Formuation, Pohedra Anasis, and Computations Aşegü Atın Department of Industria Engineering, TOBB Universit of Economics

More information

The Radix-4 and the Class of Radix-2 s FFTs

The Radix-4 and the Class of Radix-2 s FFTs Chapter 11 The Radix- and the Cass of Radix- s FFTs The divide-and-conuer paradigm introduced in Chapter 3 is not restricted to dividing a probem into two subprobems. In fact, as expained in Section. and

More information

The Web Insider... The Best Tool for Building a Web Site *

The Web Insider... The Best Tool for Building a Web Site * The Web Insider... The Best Too for Buiding a Web Site * Anna Bee Leiserson ** Ms. Leiserson describes the types of Web-authoring systems that are avaiabe for buiding a site and then discusses the various

More information

Older people s assets: using housing equity to pay for health and aged care

Older people s assets: using housing equity to pay for health and aged care Key words: aged care; retirement savings; reverse mortgage; financia innovation; financia panning Oder peope s assets: using housing equity to pay for heath and aged care The research agenda on the ageing

More information

Advertising opportunities with the Irish National Teachers Organisation (INTO)

Advertising opportunities with the Irish National Teachers Organisation (INTO) Advertising opportunities with the Irish Nationa Teachers Organisation (INTO) 1. InTouch Magazine 2. Website 3. E Newsetter 4. INTO Members Diary: Advertising and sponsorship opportunities 5. Tips for

More information

A New Statistical Approach to Network Anomaly Detection

A New Statistical Approach to Network Anomaly Detection A New Statistica Approach to Network Anomay Detection Christian Caegari, Sandrine Vaton 2, and Michee Pagano Dept of Information Engineering, University of Pisa, ITALY E-mai: {christiancaegari,mpagano}@ietunipiit

More information

New Features in Cisco IOS 12.4

New Features in Cisco IOS 12.4 Page 1 of 5 New Features in Cisco IOS 12.4 Peter J. Wecher Introduction I'm writing this in mid-august. Things have been hot (business, weather). That means its time for my more-or-ess annua artice about

More information

The Whys of the LOIS: Credit Risk and Refinancing Rate Volatility

The Whys of the LOIS: Credit Risk and Refinancing Rate Volatility The Whys of the LOIS: Credit Risk and Refinancing Rate Voatiity Stéphane Crépey 1, and Raphaë Douady 2 1 Laboratoire Anayse et Probabiités Université d Évry Va d Essonne 9137 Évry, France 2 Centre d économie

More information

NCH Software Warp Speed PC Tune-up Software

NCH Software Warp Speed PC Tune-up Software NCH Software Warp Speed PC Tune-up Software This user guide has been created for use with Warp Speed PC Tune-up Software Version 1.xx NCH Software Technica Support If you have difficuties using Warp Speed

More information

Comparison of Traditional and Open-Access Appointment Scheduling for Exponentially Distributed Service Time

Comparison of Traditional and Open-Access Appointment Scheduling for Exponentially Distributed Service Time Journa of Heathcare Engineering Vo. 6 No. 3 Page 34 376 34 Comparison of Traditiona and Open-Access Appointment Scheduing for Exponentiay Distributed Service Chongjun Yan, PhD; Jiafu Tang *, PhD; Bowen

More information

Enhanced continuous, real-time detection, alarming and analysis of partial discharge events

Enhanced continuous, real-time detection, alarming and analysis of partial discharge events DMS PDMG-RH DMS PDMG-RH Partia discharge monitor for GIS Partia discharge monitor for GIS Enhanced continuous, rea-time detection, aarming and anaysis of partia discharge events Unrivaed PDM feature set

More information

WEBSITE ACCOUNT USER GUIDE SECURITY, PASSWORD & CONTACTS

WEBSITE ACCOUNT USER GUIDE SECURITY, PASSWORD & CONTACTS WEBSITE ACCOUNT USER GUIDE SECURITY, PASSWORD & CONTACTS Password Reset Process Navigate to the og in screen Seect the Forgot Password ink You wi be asked to enter the emai address you registered with

More information

Multi-Robot Task Scheduling

Multi-Robot Task Scheduling Proc of IEEE Internationa Conference on Robotics and Automation, Karsruhe, Germany, 013 Muti-Robot Tas Scheduing Yu Zhang and Lynne E Parer Abstract The scheduing probem has been studied extensivey in

More information

Introduction to XSL. Max Froumentin - W3C

Introduction to XSL. Max Froumentin - W3C Introduction to XSL Max Froumentin - W3C Introduction to XSL XML Documents Stying XML Documents XSL Exampe I: Hamet Exampe II: Mixed Writing Modes Exampe III: database Other Exampes How do they do that?

More information

Australian Bureau of Statistics Management of Business Providers

Australian Bureau of Statistics Management of Business Providers Purpose Austraian Bureau of Statistics Management of Business Providers 1 The principa objective of the Austraian Bureau of Statistics (ABS) in respect of business providers is to impose the owest oad

More information

WHITE PAPER BEsT PRAcTIcEs: PusHIng ExcEl BEyond ITs limits WITH InfoRmATIon optimization

WHITE PAPER BEsT PRAcTIcEs: PusHIng ExcEl BEyond ITs limits WITH InfoRmATIon optimization Best Practices: Pushing Exce Beyond Its Limits with Information Optimization WHITE Best Practices: Pushing Exce Beyond Its Limits with Information Optimization Executive Overview Microsoft Exce is the

More information

AA Fixed Rate ISA Savings

AA Fixed Rate ISA Savings AA Fixed Rate ISA Savings For the road ahead The Financia Services Authority is the independent financia services reguator. It requires us to give you this important information to hep you to decide whether

More information

NCH Software PlayPad Media Player

NCH Software PlayPad Media Player NCH Software PayPad Media Payer This user guide has been created for use with PayPad Media Payer Version 2.xx NCH Software Technica Support If you have difficuties using PayPad Media Payer pease read the

More information

Example of Credit Card Agreement for Bank of America Visa Signature and World MasterCard accounts

Example of Credit Card Agreement for Bank of America Visa Signature and World MasterCard accounts Exampe of Credit Card Agreement for Bank of America Visa Signature and Word MasterCard accounts PRICING INFORMATION Actua pricing wi vary from one cardhoder to another Annua Percentage Rates for Purchases

More information

Bi-approximation Semantics for Substructural Logic at Work

Bi-approximation Semantics for Substructural Logic at Work Bi-approximation Semantics for Substructural Logic at Work Tomoyuki Suzuki Department of Computer Science, University of Leicester Leicester, LE1 7RH, United Kingdom tomoyuki.suzuki@mcs.le.ac.uk Abstract

More information

Correspondence analysis for strong three-valued logic

Correspondence analysis for strong three-valued logic Correspondence analysis for strong three-valued logic A. Tamminga abstract. I apply Kooi and Tamminga s (2012) idea of correspondence analysis for many-valued logics to strong three-valued logic (K 3 ).

More information

Simultaneous Routing and Power Allocation in CDMA Wireless Data Networks

Simultaneous Routing and Power Allocation in CDMA Wireless Data Networks Simutaneous Routing and Power Aocation in CDMA Wireess Data Networks Mikae Johansson *,LinXiao and Stephen Boyd * Department of Signas, Sensors and Systems Roya Institute of Technoogy, SE 00 Stockhom,

More information

A Hennessy-Milner Property for Many-Valued Modal Logics

A Hennessy-Milner Property for Many-Valued Modal Logics A Hennessy-Milner Property for Many-Valued Modal Logics Michel Marti 1 Institute of Computer Science and Applied Mathematics, University of Bern Neubrückstrasse 10, CH-3012 Bern, Switzerland mmarti@iam.unibe.ch

More information

p k 2k The infinite series on the right-hand side converges rapidly to about Erdős s

p k 2k The infinite series on the right-hand side converges rapidly to about Erdős s M ath. Res. Lett. 18 (2011, no. 00, 10001 10017 c Internationa Press 2011 THE SMALLEST INERT PRIME IN A CYCLIC NUMBER FIELD OF PRIME DEGREE Pau Poack Abstract. Fix an odd prime. For each cycic extension

More information

THE AVERAGE DEGREE OF AN IRREDUCIBLE CHARACTER OF A FINITE GROUP

THE AVERAGE DEGREE OF AN IRREDUCIBLE CHARACTER OF A FINITE GROUP THE AVERAGE DEGREE OF AN IRREDUCIBLE CHARACTER OF A FINITE GROUP by I. M. Isaacs Mathematics Department University of Wisconsin 480 Lincoln Dr. Madison, WI 53706 USA E-Mail: isaacs@math.wisc.edu Maria

More information

Avaya Remote Feature Activation (RFA) User Guide

Avaya Remote Feature Activation (RFA) User Guide Avaya Remote Feature Activation (RFA) User Guide 03-300149 Issue 5.0 September 2007 2007 Avaya Inc. A Rights Reserved. Notice Whie reasonabe efforts were made to ensure that the information in this document

More information

Normalization of Database Tables. Functional Dependency. Examples of Functional Dependencies: So Now what is Normalization? Transitive Dependencies

Normalization of Database Tables. Functional Dependency. Examples of Functional Dependencies: So Now what is Normalization? Transitive Dependencies ISM 602 Dr. Hamid Nemati Objectives The idea Dependencies Attributes and Design Understand concepts normaization (Higher-Leve Norma Forms) Learn how to normaize tabes Understand normaization and database

More information

READING A CREDIT REPORT

READING A CREDIT REPORT Name Date CHAPTER 6 STUDENT ACTIVITY SHEET READING A CREDIT REPORT Review the sampe credit report. Then search for a sampe credit report onine, print it off, and answer the questions beow. This activity

More information

Income Protection Solutions. Policy Wording

Income Protection Solutions. Policy Wording Income Protection Soutions Poicy Wording Wecome to Aviva This booket tes you a you need to know about your poicy, incuding: what to do if you need to caim what s covered, and expanations of some of the

More information

Art of Java Web Development By Neal Ford 624 pages US$44.95 Manning Publications, 2004 ISBN: 1-932394-06-0

Art of Java Web Development By Neal Ford 624 pages US$44.95 Manning Publications, 2004 ISBN: 1-932394-06-0 IEEE DISTRIBUTED SYSTEMS ONLINE 1541-4922 2005 Pubished by the IEEE Computer Society Vo. 6, No. 5; May 2005 Editor: Marcin Paprzycki, http://www.cs.okstate.edu/%7emarcin/ Book Reviews: Java Toos and Frameworks

More information

n k=1 k=0 1/k! = e. Example 6.4. The series 1/k 2 converges in R. Indeed, if s n = n then k=1 1/k, then s 2n s n = 1 n + 1 +...

n k=1 k=0 1/k! = e. Example 6.4. The series 1/k 2 converges in R. Indeed, if s n = n then k=1 1/k, then s 2n s n = 1 n + 1 +... 6 Series We call a normed space (X, ) a Banach space provided that every Cauchy sequence (x n ) in X converges. For example, R with the norm = is an example of Banach space. Now let (x n ) be a sequence

More information

NCH Software Crescendo Music Notation Editor

NCH Software Crescendo Music Notation Editor NCH Software Crescendo Music Notation Editor This user guide has been created for use with Crescendo Music Notation Editor Version 1.xx NCH Software Technica Support If you have difficuties using Crescendo

More information

Undergraduate Notes in Mathematics. Arkansas Tech University Department of Mathematics

Undergraduate Notes in Mathematics. Arkansas Tech University Department of Mathematics Undergraduate Notes in Mathematics Arkansas Tech University Department of Mathematics An Introductory Single Variable Real Analysis: A Learning Approach through Problem Solving Marcel B. Finan c All Rights

More information

Information Technology in Higher Education:

Information Technology in Higher Education: Information Technoogy in Higher Education: 2010 THE CHRONICLE OF HIGHER EDUCATION 2010 Survey of Chief Information Officers THE CHRONICLE Leadership Board for CIO s THE CHRONICLE LEADERSHIP BOARD FOR

More information

The epistemic structure of de Finetti s betting problem

The epistemic structure of de Finetti s betting problem The epistemic structure of de Finetti s betting problem Tommaso Flaminio 1 Hykel Hosni 2 1 IIIA - CSIC Universitat Autonoma de Barcelona (Spain) tommaso@iiia.csic.es www.iiia.csic.es/ tommaso 2 SNS Scuola

More information

GREEN: An Active Queue Management Algorithm for a Self Managed Internet

GREEN: An Active Queue Management Algorithm for a Self Managed Internet : An Active Queue Management Agorithm for a Sef Managed Internet Bartek Wydrowski and Moshe Zukerman ARC Specia Research Centre for Utra-Broadband Information Networks, EEE Department, The University of

More information

On strong fairness in UNITY

On strong fairness in UNITY On strong fairness in UNITY H.P.Gumm, D.Zhukov Fachbereich Mathematik und Informatik Philipps Universität Marburg {gumm,shukov}@mathematik.uni-marburg.de Abstract. In [6] Tsay and Bagrodia present a correct

More information

Sorting, Merge Sort and the Divide-and-Conquer Technique

Sorting, Merge Sort and the Divide-and-Conquer Technique Inf2B gorithms and Data Structures Note 7 Sorting, Merge Sort and the Divide-and-Conquer Technique This and a subsequent next ecture wi mainy be concerned with sorting agorithms. Sorting is an extremey

More information

NCH Software BroadCam Video Streaming Server

NCH Software BroadCam Video Streaming Server NCH Software BroadCam Video Streaming Server This user guide has been created for use with BroadCam Video Streaming Server Version 2.xx NCH Software Technica Support If you have difficuties using BroadCam

More information

This asserts two sets are equal iff they have the same elements, that is, a set is determined by its elements.

This asserts two sets are equal iff they have the same elements, that is, a set is determined by its elements. 3. Axioms of Set theory Before presenting the axioms of set theory, we first make a few basic comments about the relevant first order logic. We will give a somewhat more detailed discussion later, but

More information

Vision Helpdesk Client Portal User Guide

Vision Helpdesk Client Portal User Guide Hepdesk Hepdesk Vision Hepdesk Cient Porta User Guide VISION HELPDESK v3 User Guide (for Cient) CLIENT PORTAL DETAILS VISION HELPDESK v3 User Guide (for Cient) Hepdesk Index Cient Porta.....................................................

More information

INDUSTRIAL AND COMMERCIAL

INDUSTRIAL AND COMMERCIAL Finance TM NEW YORK CITY DEPARTMENT OF FINANCE TAX & PARKING PROGRAM OPERATIONS DIVISION INDUSTRIAL AND COMMERCIAL ABATEMENT PROGRAM PRELIMINARY APPLICATION AND INSTRUCTIONS Mai to: NYC Department of Finance,

More information

Advanced ColdFusion 4.0 Application Development - 3 - Server Clustering Using Bright Tiger

Advanced ColdFusion 4.0 Application Development - 3 - Server Clustering Using Bright Tiger Advanced CodFusion 4.0 Appication Deveopment - CH 3 - Server Custering Using Bri.. Page 1 of 7 [Figures are not incuded in this sampe chapter] Advanced CodFusion 4.0 Appication Deveopment - 3 - Server

More information

SABRe B2.1: Design & Development. Supplier Briefing Pack.

SABRe B2.1: Design & Development. Supplier Briefing Pack. SABRe B2.1: Design & Deveopment. Suppier Briefing Pack. 2013 Ros-Royce pc The information in this document is the property of Ros-Royce pc and may not be copied or communicated to a third party, or used

More information

Network/Communicational Vulnerability

Network/Communicational Vulnerability Automated teer machines (ATMs) are a part of most of our ives. The major appea of these machines is convenience The ATM environment is changing and that change has serious ramifications for the security

More information

IEICE TRANS. INF. & SYST., VOL.E200 D, NO.1 JANUARY 2117 1

IEICE TRANS. INF. & SYST., VOL.E200 D, NO.1 JANUARY 2117 1 IEICE TRANS. INF. & SYST., VOL.E200 D, NO. JANUARY 27 PAPER Specia Issue on Information Processing Technoogy for web utiization A new simiarity measure to understand visitor behavior in a web site Juan

More information

The Ergodic Theorem and randomness

The Ergodic Theorem and randomness The Ergodic Theorem and randomness Peter Gács Department of Computer Science Boston University March 19, 2008 Peter Gács (Boston University) Ergodic theorem March 19, 2008 1 / 27 Introduction Introduction

More information

3.5 Pendulum period. 2009-02-10 19:40:05 UTC / rev 4d4a39156f1e. g = 4π2 l T 2. g = 4π2 x1 m 4 s 2 = π 2 m s 2. 3.5 Pendulum period 68

3.5 Pendulum period. 2009-02-10 19:40:05 UTC / rev 4d4a39156f1e. g = 4π2 l T 2. g = 4π2 x1 m 4 s 2 = π 2 m s 2. 3.5 Pendulum period 68 68 68 3.5 Penduum period 68 3.5 Penduum period Is it coincidence that g, in units of meters per second squared, is 9.8, very cose to 2 9.87? Their proximity suggests a connection. Indeed, they are connected

More information

4.1 Modules, Homomorphisms, and Exact Sequences

4.1 Modules, Homomorphisms, and Exact Sequences Chapter 4 Modules We always assume that R is a ring with unity 1 R. 4.1 Modules, Homomorphisms, and Exact Sequences A fundamental example of groups is the symmetric group S Ω on a set Ω. By Cayley s Theorem,

More information

The width of single glazing. The warmth of double glazing.

The width of single glazing. The warmth of double glazing. Therma Insuation CI/SfB (31) Ro5 (M5) September 2012 The width of singe gazing. The warmth of doube gazing. Pikington Spacia Revoutionary vacuum gazing. Image courtesy of Lumen Roofight Ltd. Pikington

More information

ON COMPLETELY CONTINUOUS INTEGRATION OPERATORS OF A VECTOR MEASURE. 1. Introduction

ON COMPLETELY CONTINUOUS INTEGRATION OPERATORS OF A VECTOR MEASURE. 1. Introduction ON COMPLETELY CONTINUOUS INTEGRATION OPERATORS OF A VECTOR MEASURE J.M. CALABUIG, J. RODRÍGUEZ, AND E.A. SÁNCHEZ-PÉREZ Abstract. Let m be a vector measure taking values in a Banach space X. We prove that

More information

Journal of Economic Behavior & Organization

Journal of Economic Behavior & Organization Journa of Economic Behavior & Organization 85 (23 79 96 Contents ists avaiabe at SciVerse ScienceDirect Journa of Economic Behavior & Organization j ourna ho me pag e: www.esevier.com/ocate/j ebo Heath

More information

Oligopoly in Insurance Markets

Oligopoly in Insurance Markets Oigopoy in Insurance Markets June 3, 2008 Abstract We consider an oigopoistic insurance market with individuas who differ in their degrees of accident probabiities. Insurers compete in coverage and premium.

More information

Vacancy Rebate Supporting Documentation Checklist

Vacancy Rebate Supporting Documentation Checklist Vacancy Rebate Supporting Documentation Checkist The foowing documents are required and must accompany the vacancy rebate appication at the time of submission. If the vacancy is a continuation from the

More information

ON TWISTED HOMOGENEOUS RACKS OF TYPE D. Dedicado a Hans-Jürgen Schneider en ocasión de sus 65 años.

ON TWISTED HOMOGENEOUS RACKS OF TYPE D. Dedicado a Hans-Jürgen Schneider en ocasión de sus 65 años. REVISTA DE LA UNIÓN MATEMÁTICA ARGENTINA Voumen 51, Número 2, 2010, Páginas 1 16 ON TWISTED HOMOGENEOUS RACKS OF TYPE D N. ANDRUSKIEWITSCH, F. FANTINO, G. A. GARCÍA AND L. VENDRAMIN Abstract. We deveop

More information

SNMP Reference Guide for Avaya Communication Manager

SNMP Reference Guide for Avaya Communication Manager SNMP Reference Guide for Avaya Communication Manager 03-602013 Issue 1.0 Feburary 2007 2006 Avaya Inc. A Rights Reserved. Notice Whie reasonabe efforts were made to ensure that the information in this

More information

On General Laws of Complex Networks

On General Laws of Complex Networks On Genera Laws of Compex etwors Wenjun Xiao, Limin Peng, an ehrooz Parhami 3 Schoo of Software Engineering, South China University of Technoogy, Guangzhou 5064, P.R. China wjxiao@scut.eu.cn Department

More information

THE TEACHING ABOUT RELIGION AT SLOVENE PUBLIC SCHOOLS

THE TEACHING ABOUT RELIGION AT SLOVENE PUBLIC SCHOOLS THE TEACHING ABOUT RELIGION AT SLOVENE PUBLIC SCHOOLS Zdenko Kodeja Educationa Research Institute Ljubjana, Sovenia The teaching about reigion at pubic schoos in Sovenia is, from a ega point of view, simiar

More information

COMMUTATIVITY DEGREES OF WREATH PRODUCTS OF FINITE ABELIAN GROUPS

COMMUTATIVITY DEGREES OF WREATH PRODUCTS OF FINITE ABELIAN GROUPS COMMUTATIVITY DEGREES OF WREATH PRODUCTS OF FINITE ABELIAN GROUPS IGOR V. EROVENKO AND B. SURY ABSTRACT. We compute commutativity degrees of wreath products A B of finite abelian groups A and B. When B

More information

ENERGY AND BOLTZMANN DISTRIBUTIONS

ENERGY AND BOLTZMANN DISTRIBUTIONS MISN--159 NRGY AND BOLTZMANN DISTRIBUTIONS NRGY AND BOLTZMANN DISTRIBUTIONS by J. S. Kovacs and O. McHarris Michigan State University 1. Introduction.............................................. 1 2.

More information

Online Media Information

Online Media Information Onine Media Information www.sciencedirect.com The vita daiy source for 16 miion researchers and scientists around the gobe 70 miion pageviews each month Broad advertising product portfoio SciVerse ScienceDirect:

More information

Virtual trunk simulation

Virtual trunk simulation Virtua trunk simuation Samui Aato * Laboratory of Teecommunications Technoogy Hesinki University of Technoogy Sivia Giordano Laboratoire de Reseaux de Communication Ecoe Poytechnique Federae de Lausanne

More information

Law Libraries in the Cloud **

Law Libraries in the Cloud ** LAW LIBRARY JOURNAL Vo. 101:2 [2009-15] Technoogy for Everyone... * Law Libraries in the Coud ** Diane Murey *** Ms. Murey provides an overview of the meanings of coud computing and software as a service,

More information

ELECTRONIC FUND TRANSFERS YOUR RIGHTS AND RESPONSIBILITIES. l l

ELECTRONIC FUND TRANSFERS YOUR RIGHTS AND RESPONSIBILITIES. l l ELECTRONIC FUND TRANSFERS YOUR RIGHTS AND RESPONSIBILITIES The Eectronic Fund Transfers we are capabe of handing for consumers are indicated beow some of which may not appy your account Some of these may

More information

The epistemic structure of de Finetti s betting problem

The epistemic structure of de Finetti s betting problem The epistemic structure of de Finetti s betting problem Tommaso Flaminio 1 and Hykel Hosni 2 1 IIIA - CSIC Campus de la Univ. Autònoma de Barcelona s/n 08193 Bellaterra, Spain. Email: tommaso@iiia.csic.es

More information

Non-Archimedean Probability and Conditional Probability; ManyVal2013 Prague 2013. F.Montagna, University of Siena

Non-Archimedean Probability and Conditional Probability; ManyVal2013 Prague 2013. F.Montagna, University of Siena Non-Archimedean Probability and Conditional Probability; ManyVal2013 Prague 2013 F.Montagna, University of Siena 1. De Finetti s approach to probability. De Finetti s definition of probability is in terms

More information

l l ll l l Exploding the Myths about DETC Accreditation A Primer for Students

l l ll l l Exploding the Myths about DETC Accreditation A Primer for Students Expoding the Myths about DETC Accreditation A Primer for Students Distance Education and Training Counci Expoding the Myths about DETC Accreditation: A Primer for Students Prospective distance education

More information

FACTORING POLYNOMIALS IN THE RING OF FORMAL POWER SERIES OVER Z

FACTORING POLYNOMIALS IN THE RING OF FORMAL POWER SERIES OVER Z FACTORING POLYNOMIALS IN THE RING OF FORMAL POWER SERIES OVER Z DANIEL BIRMAJER, JUAN B GIL, AND MICHAEL WEINER Abstract We consider polynomials with integer coefficients and discuss their factorization

More information