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Volume 28 (1985)

1985
*
Annals of Pure and Applied Logic
*

., Non-closure

doi:10.1016/0168-0072(85)90022-3
fatcat:gypuekeywjbijgs27tjo3jyryu
*of*the image model and absence*of*fixed points TERLOUW, J.,*Reduction**of**higher**type**levels**by**means**of**an**ordinal**analysis**of**finite**terms*WOOD, C., see SARACINO, D. ... ., Fragments*of*arithmetic SIMPSON, S.G., see FRIEDMAN, H.M. SMITH, R.L., see FRIEDMAN, H.M. ...##
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Page 611 of Mathematical Reviews Vol. , Issue 87b
[page]

1987
*
Mathematical Reviews
*

Mints (RZhMat 1985:12 A25)
87b:03132
Terlouw, Jan (NL-GRON) 87b:03133

*Reduction**of**higher**type**levels**by**means**of**an**ordinal**analysis**of**finite**terms*. Ann. Pure Appl. Logic 28 (1985), no. 1, 73-102. ... , say*of*a functional ®, contains subdefinitions in which auxiliary functionals*of**higher**type**levels*than ® are introduced*by*primitive or transfinite recursion, then these ‘detours through*higher**type*...##
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Formal verification of a partial-order reduction technique for model checking
[chapter]

1996
*
Lecture Notes in Computer Science
*

First, this

doi:10.1007/3-540-61042-1_48
fatcat:mzcv3l3bgbbbvpllnzgynp6zg4
*reduction*technique has been implemented in the protocol*analysis*tool SPIN to significantly speed up the*analysis**of*many practical protocols; hence its correctness has important practical ... As a case study, we use the mechanical theorem prover HOL to verify the correctness*of*a partial-order*reduction*technique for cutting down the amount*of*state search performed*by*model checkers. ... Acknowledgements We would like to thank Elsa Gunter for her penetrating remarks (especially regarding the formalization*of*deterministic transition systems), and Rajeev Alur, Gerard Holzmann, Doug Howe ...##
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NOMINALISTIC ORDINALS, RECURSION ON HIGHER TYPES, AND FINITISM

2019
*
Bulletin of Symbolic Logic
*

The idea that recursion on

doi:10.1017/bsl.2018.91
fatcat:aysfqpegergxfirhqrzl2c52a4
*higher**types*could be used to simulate the limit-building in transfinite recursion seems to originate from Bernays. ... Gentzen's method*of*arithmetising*ordinals*and thus avoiding the Platonistic metaphysics*of*set theory traces back to the 1920s, when Bernays and David Hilbert used the method for*an*attempted proof*of*... This*level**of*abstraction only involves*finite*composition*of**finite*sequences in a similar manner to the construction*of**finite*exponentiation*of**ordinals*. ...##
###
Gödel's Functional ("Dialectica") Interpretation
[chapter]

1998
*
Studies in Logic and the Foundations of Mathematics
*

The language

doi:10.1016/s0049-237x(98)80020-7
fatcat:nzhyeybbwjecnhnzg47rea2tnq
*of*T is said to be*of**finite**type*since every*type*is assigned a*finite**level**by*this convention. The pure*types*(n) are defined*by*1. (0) = 0 2. (n + 1) = (n) → 0. ...*finite**type*but with values*of**type*0 only, such that each F in KL is defined*by*a*term*in T , while each*term*t in T is represented*by**an*F in KL either directly (if it is*of**type*0) or*by*abstraction ...*Terms**of**type*Π x∈σ τ denote functions f which take elements a*of**type*σ to elements f (a)*of**type*τ [a/x], and*terms**of**type*Σ x∈σ τ denote pairs a, b , where a is*an*object*of**type*σ and b is*an*object ...##
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Análise de dados ordinais em estudos clínicos e experimentais

2020
*
Jornal Vascular Brasileiro
*

Certain phenomena are represented

doi:10.1590/1677-5449.200185
fatcat:bqkiclnhwjgl7k5tt3cdsyvcga
*by*qualitative data in which each category has a hierarchical relationship to the others (for example, educational*level*, functional class, phototype, and severity*of*... This has even more influence on the results if a study's dependent variable is*an**ordinal*variable. ...*analysis**of**ordinal*data. 4, 13, [15] [16] [17] [18] [19] Table 2 illustrates*an**analysis**of*frequency*by*educational*level*, using these*ordinal*methods. ...##
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The Axiom of Choice and the Class of Hyperarithmetic Functions

1962
*
Indagationes Mathematicae (Proceedings)
*

Research for this paper was partially supported

doi:10.1016/s1385-7258(62)50029-2
fatcat:w3w7cbc3afacjk2ikydnf7ompm
*by*the Office*of*Ordnance Research under contract DA-04-200-0RD-997. 21 Series A S[P(n), m] (*by*the assumed premise*of*the comprehension axiom) we have ( ... 1.5.1*of*[7] , and the special case above is stated in my supplement to [7] . ... For, since the range*of*the quantifiers*of**level*a is well defined only if a is*an**ordinal*, the hierarchies up to co1 use as a*means**of**reduction*not only the concept*of*natural number, but also the (impredicative ...##
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The prediction error in CLS and PLS: the importance of feature selection prior to multivariate calibration

2005
*
Journal of Chemometrics
*

It is shown, however, that for a

doi:10.1002/cem.915
fatcat:lszqt7hvczbvdnnpycz4hv5tfm
*finite*training set with n samples in p dimensions there are additional error*terms*that depend on r 2 p 2 =n 2 , where r is the noise*level*per co-*ordinate*. ... This paper presents*an*asymptotically exact mathematical*analysis**of*the*mean*squared error*of*prediction*of*CLS and PLS under the linear mixture model commonly assumed in spectroscopy. ... The interesting property we find is that, although the 1=n*term*is typically multiplied*by**an*Oð1Þ coefficient, the 1=n 2*term*is multiplied*by*2 p 2 , where is the noise per co-*ordinate*and p is the dimensionality ...##
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Godel's interpretation of intuitionism

2006
*
Philosophia Mathematica
*

He founded his theory

doi:10.1093/philmat/nkj004
fatcat:cpyo4pacyfh2jo5khqebcwvzui
*of*primitive recursive functions, in which the interpretation is given, on the concept*of*computable function*of**finite**type*. ... I received helpful comments on all*of*these occasions. 1 As for the history*of*the idea*of*a hierarchy*of**types*, I know only*of*these examples: The hierarchy*of*transfinite*types*in which the natural numbers ...*An*alternative foundation for T is to introduce the so-called 'minimal*term*model', in which the objects*of**type*A are just the closed*terms**of*T*of**type*A and the*meaning**of*equations between such*terms*...##
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On Relating Theories: Proof-Theoretical Reduction
[chapter]

2019
*
Mathesis Universalis, Computability and Proof
*

The notion

doi:10.1007/978-3-030-20447-1_16
fatcat:loptt6g2jfbmtdczu2qypbk2vu
*of*proof-theoretical or finitistic*reduction**of*one theory to another has a long tradition. ... Thus we have a beautiful example*of*Hilbert's program at work, exemplifying the Hilbertian goal*of*moving from the ideal to the real*by*eliminating ideal elements. ... was supported*by*a University Research Scholarship*of*the University*of*Leeds. ...##
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Analysis of a guard condition in type theory
[chapter]

1998
*
Lecture Notes in Computer Science
*

We show that the proposed

doi:10.1007/bfb0053541
fatcat:dlvmnffdtrf4jhqlikgvabl6by
*type*system subsumes those studied*by*Coquand and Gimenez while still enjoying the basic syntactic properties*of*subject*reduction*and strong normalization with respect to a confluent ... These recursive definitions are needed to introduce 'infinite' and 'total' objects*of*coinductive*type*such as*an*infinite stream, a digital transducer, or a nonterminating process. ... Acknowledgement The first author would like to thank Eduardo Gimenez for providing the simply*typed*formulation*of*Iris system and explaining its motivations, and Alexandra Bac for a number*of*discussions ...##
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Type-based termination of generic programs

2009
*
Science of Computer Programming
*

They are partially ordered; the order is given

doi:10.1016/j.scico.2008.01.004
fatcat:b53ufp6afbhnzjm2d3tqcojzqq
*by*• ≤ p and p ≤ p. Kinds κ are the "*types*"*of**type*constructors. ... In F ω , size expressions belong to the*type*language and have kind ord. κ ::= **types*| ord*ordinals*| pκ 1 → κ 2 co-/contra-/mixed-variant constructor transformers Notation: κ p ... This research has been supported*by*the coordination action*TYPES*(510996) and thematic network Applied Semantics II (IST-2001-38957)*of*the European Union and the project Cover*of*the Swedish Foundation ...##
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Ordinal Arithmetic: A Case Study for Rippling in a Higher Order Domain
[chapter]

2001
*
Lecture Notes in Computer Science
*

*Ordinal*arithmetic provides a natural set

*of*

*higher*order examples on which transfinite induction may be attempted using rippling. ...

*Ordinal*arithmetic provides a natural set

*of*

*higher*order examples on which transfinite induction may be attempted using rippling. ... ∀α : ordl. α is

*an*

*ordinal*We introduce here the

*type*

*of*

*ordinals*, ordl; as is well known, this cannot correspond to a set. Definition 5. ...

##
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Integrating Ontology into SBVR

2006
*
Social Science Research Network
*

Representation-the connection between expression and a

doi:10.2139/ssrn.906579
fatcat:vwknuijbtvfi7pv5s56sc43r7u
*meaning*or a portrayal*of*a*meaning**by**an*expression. ... Exclusion Difference scaled & Subtypes Patterns*of*separation in*terms**of*ratios*of*separation (eg: Physical distance)*Ordinal*& Subtypes Patterns*of*separation in*terms**of*quantitative differences ...##
###
ERA ranking representability: The missing link between ordinal regression and multi-class classification

2011
*
2011 11th International Conference on Intelligent Systems Design and Applications
*

For the three-class case, this results in a new

doi:10.1109/isda.2011.6121820
dblp:conf/isda/WaegemanB11
fatcat:5uyc2kuh5bg6pmq4drprwhv4ke
*type**of*cycle transitivity for pairwise AUCs that can be verified*by*solving*an*integer quadratic program. ... As performance measure, we use the area under the ROC curve (AUC) and its reformulation in*terms**of*graphs. ... ACKNOWLEDGMENT W.W. is supported as a postdoc*by*the Research Foundation*of*Flanders (FWO-Vlaanderen). ...
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