Search results for "Action axiom"

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Learning with belief levels

2008

AbstractWe study learning of predicate logics formulas from “elementary facts,” i.e. from the values of the predicates in the given model. Several models of learning are considered, but most of our attention is paid to learning with belief levels. We propose an axiom system which describes what we consider to be a human scientist's natural behavior when trying to explore these elementary facts. It is proved that no such system can be complete. However we believe that our axiom system is “practically” complete. Theorems presented in the paper in some sense confirm our hypothesis.

CompletenessAxiom systemsbusiness.industryComputer Networks and CommunicationsApplied Mathematics010102 general mathematicsInductive inference02 engineering and technologyInductive reasoning01 natural sciencesBelief levelsPredicate (grammar)EpistemologyTheoretical Computer ScienceTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESComputational Theory and Mathematics020204 information systems0202 electrical engineering electronic engineering information engineeringLearningArtificial intelligence0101 mathematicsbusinessAction axiomAxiomMathematicsJournal of Computer and System Sciences
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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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