Search results for "Axiom of extensionality"

showing 4 items of 4 documents

Axiomatic characterization of the weighted solidarity values

2014

Abstract We define and characterize the class of all weighted solidarity values . Our first characterization employs the classical axioms determining the solidarity value (except symmetry ), that is, efficiency , additivity and the A-null player axiom , and two new axioms called proportionality and strong individual rationality . In our second axiomatization, the additivity and the A-null player axioms are replaced by a new axiom called average marginality .

Discrete mathematicsSociology and Political ScienceAxiom independenceGeneral Social SciencesProportionality (mathematics)RationalitySolidarityEconomia Aspectes psicològicsAxiom of extensionalityMathematics::LogicEconomia matemàticaAdditive functionStatistics Probability and UncertaintyMathematical economicsGeneral PsychologyAxiomMathematics
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Rapid construction of algebraic axioms from samples

1991

Abstract An axiom is called reliable if it is confirmed in several places in a given sample of algebra. A very effective algorithm for enumerating such axioms is described.

General Computer ScienceTheorySample (material)Theoretical Computer ScienceSeparation axiomAlgebraAxiom of extensionalityMathematics::LogicConstruction of the real numbersTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESTheoryofComputation_LOGICSANDMEANINGSOFPROGRAMSComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONCalculusReverse mathematicsAlgebraic numberAxiomComputer Science(all)MathematicsTheoretical Computer Science
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Generalized Rough Sets in Contextual Spaces

1997

This paper presents a generalization of Pawlak’s conception of rough sets [6] and [7]. It is more general than Pawlak’s solution of the problem of the definability of sets, the knowledge of which is incomplete and vague. The authors’ conception is based on conception of contextual space [4], which was inspired by Ziarko’s approach [12] to rough sets. Rough sets introduced by Pawlak [6] are particular cases of contextual rough sets defined in the contextual approximation space. This space is defined axiomatically by means of so called context relations. Every contextual rough set determined by set X can be determined by the union of the lower approximation of X and a subset of the boundary o…

Set (abstract data type)AlgebraAxiom of extensionalityGeneralizationBoundary (topology)Context (language use)Rough setSpace (commercial competition)Element (category theory)Mathematics
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Towards Axiomatic Basis of Inductive Inference

2001

The language for the formulation of the interesting statements is, of course, most important. We use first order predicate logic. Our main achievement in this paper is an axiom system which we believe to be more powerful than any other natural general purpose discovery axiom system. We prove soundness of this axiom system in this paper. Additionally we prove that if we remove some of the requirements used in our axiom system, the system becomes not sound. We characterize the complexity of the quantifier prefix which guaranties provability of a true formula via our system. We prove also that if a true formula contains only monadic predicates, our axiom system is capable to prove this formula…

SoundnessDiscrete mathematicsPredicate logicSMorse–Kelley set theoryComputer scienceNon-well-founded set theoryZermelo–Fraenkel set theoryConstructive set theoryInductive reasoningAxiom schemaUrelementScott's trickMonad (functional programming)First-order logicAxiom of extensionalityMathematics::LogicTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESTheoryofComputation_LOGICSANDMEANINGSOFPROGRAMSCalculusAxiom of projective determinacyAxiom of choiceKripke–Platek set theoryAction axiomAxiom
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