scholarly journals Logical Classification of Partially Ordered Data

2019 ◽  
pp. 115-126
Author(s):  
Elena V. Djukova ◽  
Gleb O. Masliakov ◽  
Petr A. Prokofyev
Keyword(s):  
Partially Ordered ◽  
Ordered Data

scholarly journals Rank Tests from Partially Ordered Data Using Importance and MCMC Sampling Methods

2016 ◽  
Vol 31 (3) ◽  
pp. 325-347
Author(s):  
Debashis Mondal ◽  
Nina Hinrichs
Keyword(s):  
Sampling Methods ◽  
Rank Tests ◽  
Partially Ordered ◽  
Mcmc Sampling ◽  
Ordered Data

scholarly journals Longitudinal partially ordered data analysis for preclinical sarcopenia

2020 ◽  
Vol 39 (24) ◽  
pp. 3313-3328
Author(s):  
Edward H. Ip ◽  
Shyh‐Huei Chen ◽  
Karen Bandeen‐Roche ◽  
Jaime L. Speiser ◽  
Li Cai ◽  
...  
Keyword(s):  
Data Analysis ◽  
Partially Ordered ◽  
Ordered Data

Classification of involutions on finitary incidence algebras

2014 ◽  
Vol 24 (08) ◽  
pp. 1085-1098 ◽  
Author(s):  
Rosali Brusamarello ◽  
Érica Zancanella Fornaroli ◽  
Ednei Aparecido Santulo
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Sufficient Conditions ◽  
Decomposition Theorem ◽  
Multilinear Algebra ◽  
Partially Ordered ◽  
Incidence Algebras ◽  
Linear Multilinear Algebra ◽  
Necessary And Sufficient

Let X be a connected partially ordered set and let K be a field of characteristic different from 2. We present necessary and sufficient conditions for two involutions on the finitary incidence algebra of X over K, FI (X), to be equivalent in the case when every multiplicative automorphism of FI (X) is inner. To get the classification of involutions we extend the concept of multiplicative automorphism to finitary incidence algebras and prove the Decomposition Theorem of involutions of [Anti-automorphisms and involutions on (finitary) incidence algebras, Linear Multilinear Algebra 60 (2012) 181–188] for finitary incidence algebras.

scholarly journals Ford's Procedure for Combining Multiple Sets of Partially Ordered Data

1973 ◽  
Vol 33 (1) ◽  
pp. 43-52
Author(s):  
Frank M. Andrews ◽  
Donald C. Pelz
Keyword(s):  
Partially Ordered ◽  
Ordered Data

Lattice embeddings into the recursively enumerable degrees

1986 ◽  
Vol 51 (2) ◽  
pp. 257-272 ◽  
Author(s):  
K. Ambos-Spies ◽  
M. Lerman
Keyword(s):  
Elementary Theory ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Classification Problems ◽  
Partially Ordered ◽  
Recursively Enumerable ◽  
Existential Theory ◽  
Finite Lattices ◽  
Binary Relation Symbol

The classification of algebraic structures which can be embedded into ℛ, the uppersemilattice of recursively enumerable degrees, is the key to answering certain questions about Th(ℛ), the elementary theory of ℛ. In particular, these classification problems are important for answering decidability questions about fragments of Th(ℛ). Thus the solutions of Fried berg [F] and Mučnik [M] to Post's problem were easily extended to show that all finite partially ordered sets are embeddable into ℛ, and hence that ∃1 ∩ Th(ℛ), the existential theory of ℛ, is decidable. (The language used is ℒ′, the pure predicate calculus together with a binary relation symbol ≤ to be interpreted as the ordering of ℛ) The problem of determining which finite lattices are embeddable into ℛ has been a long-standing open problem, and is one of the major obstacles to determining whether ∀2 ∩ Th(ℛ), the universal-existential theory of ℛ, is decidable. Shore has obtained some nice partial results in this direction. Embeddings also played a central role in showing that Th(ℛ) is not ℵ0-categorical (Lerman, Shore and Soare [LeShSo]), thus resolving a problem posed by Jockusch. Harrington and Shelah [HS] embedded all 0′-presentable partially ordered sets into ℛ in such a way that the partially ordered sets can be uniformly recovered from four parameters. They used these embeddings to show that Th(ℛ) is undecidable.The first nontrivial extension of the embeddings of Friedberg and Mučnik to lattice embeddings was obtained independently by Lachlan [La1] and Yates [Y] who showed that the four-element Boolean algebra can be embedded into ℛ. Thomason [T] and Lerman independently extended this result to include all finite distributive lattices. The nondistributive case, however, was much more difficult. Lachlan [La2] embedded the two five-element nondistributive lattices M5 and N5 (see Figures 1 and 2) into ℛ, and his proof could easily have been extended to include a larger class of lattices.

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