Abstract
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.
This project was supported by an International Agreement under NSF Grant 9421640.
Research supported by Grant No.01.0354 from the Latvian Council of Science, Contract IST-1999-11234 (QAIP) from the European Commission, and the Swedish Institute, Project ML-2000
Supported in part by NSF Grant CCR-9732692
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Bārzdiņš, J., Freivalds, R., Smith, C.H. (2001). Towards Axiomatic Basis of Inductive Inference. In: Freivalds, R. (eds) Fundamentals of Computation Theory. FCT 2001. Lecture Notes in Computer Science, vol 2138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44669-9_1
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DOI: https://doi.org/10.1007/3-540-44669-9_1
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