Results 221 to 230 of about 1,688 (254)

Independence of each axiom in a set of axioms and complete sets of axioms of Boolean algebra

Proceedings 32nd IEEE International Symposium on Multiple- Valued Logic, 2003
We investigate fundamental properties of axioms of Boolean algebra in detail by using the Method of Indeterminate Coefficients. Three axioms, one of the complementary laws, one of the distributive laws and one of the least element (a), greatest element (b) and the absorption laws are essential for the algebra because those are independent from all ...
Tomoko Ninomiya, Masao Mukaidono
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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 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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The independence of Quine's axioms *200 and *201

Journal of Symbolic Logic, 1941
We refer to the axioms in Quine's book, Mathematical logic, New York, 1940.To prove the independence of *200, give xϵ α the truth value F in all cases and give (x)ϕ the same truth value as ϕ. Then clearly all formulas derivable from the other axioms besides *200 have the value T, whereas from *200 one can derive (∃x)(∃α)(xϵ α) which has the value F ...
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Independence of axioms of an associative trioid

Semigroup Forum, 2022
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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 “Huntington’s axioms” for boolean algebra

The Mathematical Gazette, 1978
Among the various logically equivalent sets of axioms for boolean algebra ([1] discusses four of them), that referred to in the title of this article is popular because of its symmetry (self-duality) and convenience in application. The textbook presentation is essentially as follows; the qualifiers ‘left’, ‘right’ are often omitted, although the ...
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Axioms of uncertainty measures: dependence and independence

Fuzzy Sets and Systems, 1990
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The Independence of Axioms of B. Russell's Logical System of Axioms

2006 World Automation Congress, 2006
By using the method of indeterminate coefficients, we can examine the independence of each axiom of a system of axioms. In this paper, we treat the Russell's classical logical system of axioms. We examine whether each axiom is independent or not from the other axioms and show the results.
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Extending Independent Sets to Bases and the Axiom of Choice

Mathematical Logic Quarterly, 1998
AbstractWe show that the both assertions “in every vector space B over a finite element field every subspace V ⊆ B has a complementary subspace S” and “for every family 𝒜 of disjoint odd sized sets there exists a subfamily ℱ={Fj:j ϵω} with a choice function” together imply the axiom of choice AC.
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