scholarly journals Reasoning with Partial Orders: Restrictions on Ignorance Inferences of Superlative Modifiers

2016 ◽  
Vol 26 ◽  
pp. 489
Author(s):  
Jon Ander Mendia
Keyword(s):  
Experimental Evidence ◽  
Ordered Set ◽  
Epistemic Possibility ◽  
Partial Orders ◽  
Partially Ordered ◽  
Totally Ordered Set ◽  
Exhaustive Interpretation

The present study is concerned with Ignorance Inferences associated with Superlative Modifiers (SMs) like at least and at most. Experimental evidence will be presented showing that the Ignorance Inferences associated with SMs depend on their associate: when the associate of an SM is a totally ordered set (e.g. a numeral), the exhaustive interpretation of the prejacent must necessarily constitute an epistemic possibility for the speaker. However, when the associate of the SM is partially ordered, the exhaustive interpretation of the prejacent can, but need not constitute an epistemic possibility for the speaker.

ON RIBBON PRESENTATIONS OF RIBBON KNOTS

1994 ◽  
Vol 03 (02) ◽  
pp. 223-231
Author(s):  
TOMOYUKI YASUDA
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Partially Ordered ◽  
Totally Ordered Set

A ribbon n-knot Kn is constructed by attaching m bands to m + 1n-spheres in the Euclidean (n + 2)-space. There are many way of attaching them; as a result, Kn has many presentations which are called ribbon presentations. In this note, we will induce a notion to classify ribbon presentations for ribbon n-knots of m-fusions (m ≥ 1, n ≥ 2), and show that such classes form a totally ordered set in the case of m = 2 and a partially ordered set in the case of m ≥ 1.

scholarly journals Endpoints inT0-Quasimetric Spaces: Part II

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Collins Amburo Agyingi ◽  
Paulus Haihambo ◽  
Hans-Peter A. Künzi
Keyword(s):  
Complete Lattice ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Partial Orders ◽  
Macneille Completion ◽  
Partially Ordered ◽  
Irreducible Elements ◽  
Quasimetric Space

We continue our work on endpoints and startpoints inT0-quasimetric spaces. In particular we specialize some of our earlier results to the case of two-valuedT0-quasimetrics, that is, essentially, to partial orders. For instance, we observe that in a complete lattice the startpoints (resp., endpoints) in our sense are exactly the completely join-irreducible (resp., completely meet-irreducible) elements. We also discuss for a partially ordered set the connection between its Dedekind-MacNeille completion and theq-hyperconvex hull of its naturalT0-quasimetric space.

Multilevel Databases

2005 ◽  
pp. 383-389 ◽  
Author(s):  
Alban Gabillon
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Dominance Relation ◽  
Multilevel Security ◽  
Partially Ordered ◽  
Totally Ordered Set ◽  
Security Levels ◽  
Clearance Level

In the context of multilevel security, every piece of information is associated with a classification level, and every user is associated with a clearance level. The classification and clearance levels are taken from the same set of security levels. This set is totally or partially ordered and forms a lattice. The ordering relation is called the dominance relation and is denoted by ³. An example of a totally ordered set is {Unclassified, Confidential, Secret} with Secret > Confidential > Unclassified. An example for a partially ordered set is {low, (Secret, NATO), (Secret, Defence), high} with (Secret, NATO) > low, (Secret, Defence) > low, high > (Secret, NATO), high > (Secret, Defence), (Secret, NATO) and (Secret, Defence) are incomparable.

Which Ordered Sets have a Complete Linear Extension?

1981 ◽  
Vol 33 (5) ◽  
pp. 1245-1254 ◽  
Author(s):  
Maurice Pouzet ◽  
Ivan Rival
Keyword(s):  
Partially Ordered Set ◽  
Linear Extension ◽  
Ordered Set ◽  
Ordered Sets ◽  
Partially Ordered ◽  
Totally Ordered Set

It is a well known and useful fact [4] that every (partially) ordered set P has a linear extension L (that is, a totally ordered set (chain) on the same underlying set as P and satisfying a ≦ b in L whenever a ≦ b in P). It is just as well known that an ordered set P can be embedded in an ordered set P′ which, in turn, has a complete linear extension L′ (that is, a linear extension in which every subset has both a supremum and an infimum); just take L′ to be the “completion by cuts” of L. However, an arbitrary ordered set P need not, itself, have a complete linear extension (for example, if P is the chain of integers or, for that matter, if P is any noncomplete chain). It is natural to ask which ordered sets have a complete linear extension?

scholarly journals Author Correction: Experimental evidence for the existence of a second partially-ordered phase of ice VI

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ryo Yamane ◽  
Kazuki Komatsu ◽  
Jun Gouchi ◽  
Yoshiya Uwatoko ◽  
Shinichi Machida ◽  
...  
Keyword(s):  
Experimental Evidence ◽  
Partially Ordered

A Correction to this paper has been published: https://doi.org/10.1038/s41467-021-22085-4

Information Retrieval Systems, an Algebraic Approach I1

1981 ◽  
Vol 4 (3) ◽  
pp. 551-603
Author(s):  
Zbigniew Raś
Keyword(s):  
Information Retrieval ◽  
Boolean Algebra ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Algebraic Approach ◽  
Partially Ordered ◽  
Retrieval Systems ◽  
Information Retrieval Systems ◽  
Present Part ◽  
L Systems

This paper is the first of the three parts of work on the information retrieval systems proposed by Salton (see [24]). The system is defined by the notions of a partially ordered set of requests (A, ⩽), the set of objects X and a monotonic retrieval function U : A → 2X. Different conditions imposed on the set A and a function U make it possible to obtain various classes of information retrieval systems. We will investigate systems in which (A, ⩽) is a partially ordered set, a lattice, a pseudo-Boolean algebra and Boolean algebra. In my paper these systems are called partially ordered information retrieval systems (po-systems) lattice information retrieval systems (l-systems); pseudo-Boolean information retrieval systems (pB-systems) and Boolean information retrieval systems (B-systems). The first part concerns po-systems and 1-systems. The second part deals with pB-systems and B-systems. In the third part, systems with a partial access are investigated. The present part discusses the method for construction of a set of attributes. Problems connected with the selectivity and minimalization of a set of attributes are investigated. The characterization and the properties of a set of attributes are given.

scholarly journals Each join-completion of a partially ordered set in the solution of a universal problem

1974 ◽  
Vol 17 (4) ◽  
pp. 406-413 ◽  
Author(s):  
Jürgen Schmidt
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Unique Extension ◽  
Partially Ordered ◽  
Special Cases

The main result of this paper is the theorem in the title. Only special cases of it seem to be known so far. As an application, we obtain a result on the unique extension of Galois connexions. As a matter of fact, it is only by the use of Galois connexions that we obtain the main result, in its present generality.

scholarly journals Primitive idempotent measures on compact semitopological semigroups

1972 ◽  
Vol 13 (4) ◽  
pp. 451-455 ◽  
Author(s):  
Stephen T. L. Choy
Keyword(s):  
Partial Order ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Zero Element ◽  
Primitive Idempotent ◽  
Natural Partial Order ◽  
Partially Ordered

For a semigroup S let I(S) be the set of idempotents in S. A natural partial order of I(S) is defined by e ≦ f if ef = fe = e. An element e in I(S) is called a primitive idempotent if e is a minimal non-zero element of the partially ordered set (I(S), ≦). It is easy to see that an idempotent e in S is primitive if and only if, for any idempotent f in S, f = ef = fe implies f = e or f is the zero element of S. One may also easily verify that an idempotent e is primitive if and only if the only idempotents in eSe are e and the zero element. We let П(S) denote the set of primitive idempotent in S.

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