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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, 2003We 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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The independence of Quine's axioms *200 and *201
Journal of Symbolic Logic, 1941We 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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Independent Axioms for Infinite-Valued Logic
Journal of Symbolic Logic, 1963Recent 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 of an associative trioid
Semigroup Forum, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The independence of “Huntington’s axioms” for boolean algebra
The Mathematical Gazette, 1978Among 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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Independence of axioms for fourgonal families
Journal of Geometry, 2001According 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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Axioms of uncertainty measures: dependence and independence
Fuzzy Sets and Systems, 1990zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Consequentialism and the Independence Axiom
1988St 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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Extending Independent Sets to Bases and the Axiom of Choice
Mathematical Logic Quarterly, 1998AbstractWe 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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The Independence of Axioms of B. Russell's Logical System of Axioms
2006 World Automation Congress, 2006By 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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