Results 251 to 260 of about 2,731 (293)

On the Axiomization of Conditional Independence

Kybernetes, 1992
Presents an investigation of some aspects of the axiomization of conditional independence of probability. Contributes to the understanding of Pearl's completeness conjecture and identifies a direction for revision which could remove some of the difficulties of Pearl's axiom set, but this alternative is not without its own difficulties.
An, Z., Bell, D. A., Hughes, J. G.
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Independent Axioms for Vector Spaces

The Mathematical Gazette, 1973
In a recent paper [1], Victor Bryant shows how the number of axioms required to define a vector space can be reduced to seven (in addition to closure requirements). The main result of his article is that commutativity of addition can be deduced from the other axioms.
Rigby, J. F., Wiegold, James
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The Congruence Axiom and Path Independence

Journal of Economic Theory, 1999
Let \(X\) be a universal set and let \([X]\) denote the collection of non-empty subsets of \(X\). The authors consider choice functions \(C:S \to [X]\), where \(S\) is a non-empty subcollection of \(X\). Let \(A \in S\). A path in \(A\) is a finite ordered collection of non-empty subsets of \(A\) covering \(A\).
Bandyopadhyay, Taradas, Sengupta, Kunal
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The equality axioms are not independent

ACM SIGACT News, 2004
After computer experiments by using the ANDP prover we showed that the five axioms for reflexivity, symmetry, transitivity and substitutivity of equality can be replaced by only two of the five axioms.
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Independent axioms for Convexity

Journal of Geometry, 1974
Join-structures or Convexity Spaces generalise the geometry of Vector Spaces by means of axioms concerning line segments. Most other generalisations of this type are just particular examples of Convexity Spaces. In the many papers on this subject the collection of axioms is too long: in this short note we exhibit an independent set of axioms for these ...
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On the independence of the axioms of definiteness (Axiome der Bestimmtheit)

Journal of Symbolic Logic, 1939
The question of the independence of the axioms of the theory of sets has been dealt with in a number of works, although not in a final manner. The writer will be concerned solely with the axiomatic system of Zermelo and Fraenkel, and only with that feature of the system whereby all the objects of the underlying domain are sets (so that there is no ...
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The Independence of a Strong Axiom of Choice

The Mathematical Gazette, 1962
There is a growing realization among mathematicians and logicians of the many-sided role played by the axiom of choice in various branches of mathematics. Many of them tend to accept the axiom of choice as a legitimate principle provided, of course, it is proved to be independent in a suitable axiom system. This tendency has been accelerated by Gödel’s
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The independence of a weak axiom of choice

Journal of Symbolic Logic, 1956
1. The purpose of this paper is to show that, if the axioms of a system G of set theory are consistent, then it is impossible to prove from them the following weak form of the axiom of choice: (H1) For every denumerable set x of disjoint two-element sets, there is a set y, called a choice set for x, which contains exactly one element in common with ...
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Independent set axioms, base axioms and circuit axioms of\\ supermatroids

SCIENTIA SINICA Mathematica, 2016
Dunstan et al. first proposed the concept of supermatroids in 1972 by generalizing the underlying sets of matroids from finite sets to finite posets. Barnabei et al. introduced another matroidal structure on posets, i.e., poset matroids. By the one-to-one correspondence between finite distributive lattices and finite posets, poset matroids are just ...
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Independent axiom schemata for S5

Journal of Symbolic Logic, 1956
Leo Simons has shown that H1—H6 below constitute a set of independent axiom schemata for S3, with detachment for material implication “→” as the only primitive rule. He also showed that addition of the scheme (◇ ◇ α ⥽ ◇ α) yields S4, and that these schemata for S4 are independent. The question for S5 was left open.
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