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Keys to First Corinthians: Revisiting the Major Issues

Jerome Murphy-O'Connor

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199564156
eISBN:
9780191721281
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199564156.001.0001
Subject:
Religion, Biblical Studies

This book brings together sixteen originally independent articles dealing with various aspects of 1 Corinthians and published between 1976 and 1993. As the series develops there are more frequent ... More


THE INTERPOLATION THEOREM IN INTUITIONISTIC PREDICATE CALCULUS

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0004
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter presents the equivalence of Craig's interpolation property to Robinson's joint consistency, and a proof of Lyndon's interpolation theorem for the classical predicate logic. It is proved ... More


INTERPOLATION AND DEFINABILITY IN QUANTIFIED LOGICS

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0005
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter contains a proof of Lyndon's interpolation property (LIP) for quantified extensions of basic modal logics K, T, D, K4, and S4, and for some others, including the propositional S5 has ... More


INTERPOLATION IN NORMAL EXTENSIONS OF THE MODAL LOGIC S4

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0008
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

It appears that the behaviour of interpolation over the modal S4 logic is similar to interpolation in superintuitionistic logics. It is shown that all extensions of S4 with interpolation property for ... More


Spatial variation in risk

Dirk U. Pfeiffer, Timothy P. Robinson, Mark Stevenson, Kim B. Stevens, David J. Rogers, and Archie C. A. Clements

in Spatial Analysis in Epidemiology

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198509882
eISBN:
9780191709128
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509882.003.0006
Subject:
Biology, Disease Ecology / Epidemiology

This chapter discusses spatial variation in risk. Epidemiological disease investigations should include an assessment of the spatial variation of disease risk, as this may provide important clues ... More


Commentary

H. A. G. Houghton

in Augustine's Text of John: Patristic Citations and Latin Gospel Manuscripts

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199545926
eISBN:
9780191719974
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199545926.003.0013
Subject:
Religion, Early Christian Studies

The textual commentary treats Augustine's text of John verse by verse, concentrating on variants from the Vulgate. There are a number of occasions on which Augustine has a reading not attested in ... More


INTRODUCTION

Pavol Hell and Jaroslav Nešetřil

in Graphs and Homomorphisms

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198528173
eISBN:
9780191713644
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528173.003.0001
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This introductory chapter is a sampler of the material covered in the book. It introduces the notation and terminology in the book, and provides motivational examples and applications, many taken up ... More


CRAIG'S THEOREM IN SUPERINTUITIONISTIC LOGICS AND AMALGAMABLE VARIETIES OF PSEUDOBOOLEAN ALGEBRAS

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0006
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter contains a full description of superintuitionistic logics with Craig's interpolation property CIP. It turns out that in the continuum of intermediate logics, only seven have Craig's ... More


ALTERNATIVE APPROACHES

D. A. Bini, G. Latouche, and B. Meini

in Numerical Methods for Structured Markov Chains

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198527688
eISBN:
9780191713286
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198527688.003.0008
Subject:
Mathematics, Numerical Analysis

Alternative numerical approaches for solving matrix equations associated with M/G/1-type Markov chains are considered in this chapter. A general shift technique for accelerating the convergence of ... More


INTERPOLATION IN MODAL INFINITE SLICE LOGICS CONTAINING THE LOGIC K4

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0010
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter examines the family NE(K) of normal extensions of K4. With any such logic L its reflexive fragment r(L) is associated, which contains the logic S4. A logic L is of infinite slice if ... More


SYNTACTIC PROOF OF INTERPOLATION FOR THE INTUITIONISTIC PREDICATE LOGIC

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0013
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter presents a syntactic proof of the Lyndon interpolation theorem for the intuitionistic predicate logic. It is a modification of a proof of the interpolation theorem found by K. Schütte, ... More


INTERPOLATION BY TRANSLATION

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0014
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter proposes some uniform algorithmic methodology for finding interpolants in various logic. It operates with translations of non-classical logics into classical first-order theories and ... More


INTERPOLATION IN (INTUITIONISTIC) LOGIC PROGRAMMING

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0015
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter provides interpolation results for the Horn clause fragment of classical or intuitionistic logic. A weak variant of interpolation for a fragment of the intuitionistic predicate logic ... More


INTERPOLATION IN GOAL- DIRECTED PROOF SYSTEMS

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0016
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter studies the interpolation properties for implicational fragment of a variety of substructural, strict modal, and intuitionistic and intermediate logics. The methodology is ... More


FURTHER RESULTS AND DISCUSSION

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0017
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses further directions of research. A brief review of the results obtained on interpolation and definability, which were not included in this volume, is presented.


Interpolations in 1 Corinthians

Jerome Murphy‐O'Connor

in Keys to First Corinthians: Revisiting the Major Issues

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199564156
eISBN:
9780191721281
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199564156.003.00016
Subject:
Religion, Biblical Studies

After a discussion of the validity of the methodology normally used to determine interpolations, i.e. additions to a text after it had left its author's hands, the chapter passes in review thirteen ... More


Finite Elements on Tetrahedra

Peter Monk

in Finite Element Methods for Maxwell's Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.003.0005
Subject:
Mathematics, Numerical Analysis

The finite element method is based on a geometric decomposition of the domain of Maxwell’s equations into simple elements. This chapter is devoted to tetrahedral elements, which are very common in ... More


Finite Elements on Hexahedra

Peter Monk

in Finite Element Methods for Maxwell's Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198508885
eISBN:
9780191708633
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508885.003.0006
Subject:
Mathematics, Numerical Analysis

An alternative to the tetrahedral elements discussed in the previous chapter is to use finite elements based on cubes, or more generally, hexahedra. Hexahedral elements have been used in several ... More


THE MATHEMATICAL SETTING

Jan Modersitzki

in Numerical Methods for Image Registration

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198528418
eISBN:
9780191713583
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528418.003.0003
Subject:
Mathematics, Applied Mathematics

The basic mathematical notation is introduced, including formal definitions of images and digital images, midpoint and meshpoint grids. Local and global interpolation techniques such as ... More


DISCRETE SYSTEMS AND FREE-DISCONTINUITY PROBLEMS

Andrea Braides

in Gamma-Convergence for Beginners

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198507840
eISBN:
9780191709890
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507840.003.0012
Subject:
Mathematics, Applied Mathematics

This chapter shows how general non-convex difference schemes can give rise to functionals defined by piecewise-Sobolev functions with interactions between surface and volume terms. Different ... More


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