6533b835fe1ef96bd129e92a

RESEARCH PRODUCT

Towards Axiomatic Basis of Inductive Inference

Rusins FreivaldsJanis BarzdinsCarl Smith

subject

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

description

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 in the considered model.

yearjournalcountryeditionlanguage
2001-01-01
https://doi.org/10.1007/3-540-44669-9_1