Results 281 to 290 of about 49,413 (326)

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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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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Asset Demand Without the Independence Axiom

Econometrica, 1989
An important application of the theory of choice under uncertainty is to asset markets, and an important property in these markets is a preference for portfolio diversification. If an investor is an expected utility maximizer, then (s)he is risk averse if and only if (s)he exhibits a preference for diversification.
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Independent Axioms for Infinite-Valued Logic

Journal of Symbolic Logic, 1963
Recent interest in Łukasiewicz' Lℵ0, raises the question whether this axiomatic system can be simplified [2]. It is known that Łukasiewicz' fourth axiom CCCPQCQPCQP is dependent [4] p. 51. The axiomatic system resulting from deleting the fourth axiom from Lℵ0 will be shown to be “minimal” in the sense that the axioms and rules of inference are mutually
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Independence of axioms for fourgonal families

Journal of Geometry, 2001
According to \textit{L. Bader} and \textit{S. E. Payne} [J. Geom. 63, No. 1-2, 1-16 (1998; Zbl 0934.51003)], four axioms characterize the elation groups \(E\) of elation generalized quadrangles: \(E\) contains a family \(S\) of subgroups and, for each \(A\in S\), another subgroup \(A^*\) containing \(A\), subject to the conditions (1) \(A^*B=E\), (2) \(
Boekholt, Sven, Stroppel, Markus
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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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Axioms of uncertainty measures: dependence and independence

Fuzzy Sets and Systems, 1990
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Consequentialism and the Independence Axiom

1988
St Thomas Aquinas wrote to the effect that no good consequences could make a bad action good, and that no bad consequences could make a good action bad. John Stuart Mill, following a utilitarian tradition, put forward exactly the contradictory hypothesis that, as a necessary condition for rationality, actions should be judged entirely by their ...
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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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