2013/08/27 by Stefano Berardi, Ugo de' Liguoro, Ugo de’ Liguoro · 1 citation
Computer Science · Mathematics · #Algorithm #Computability, Logic, AI Algorithms #Computer science #Constructive #Discrete mathematics #Fixed point #Fixed-point theorem #Machine Learning and Algorithms #Mathematical analysis #Mathematical proof #Mathematics #Monotonic function #Nondeterministic algorithm #Numerical Methods and Algorithms #Process (computing) #Space (punctuation) #State (computer science) #Theoretical computer science #cs.LO
paper · pdf · doi:10.4204/eptcs.126.1
published in Electronic Proceedings in Theoretical Computer Science 126, 1-10 (Open Publishing Association) · In Proceedings FICS 2013, arXiv:1308.5896
openalex publication_date 2013/08/27 · arxiv created 2013/09/04 · arxiv updated 2013/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We consider the problem of finding pre-fixed points of interactive realizers over arbitrary knowledge spaces, obtaining a relative recursive procedure. Knowledge spaces and interactive realizers are an abstract setting to represent learning processes, that can interpret non-constructive proofs. Atomic pieces of information of a knowledge space are stratified into levels, and evaluated into truth values depending on knowledge states. Realizers are then used to define operators that extend a given state by adding and possibly removing atoms: in a learning process states of knowledge change nonmonotonically. Existence of a pre-fixed point of a realizer is equivalent to the termination of the learning process with some state of knowledge which is free of patent contradictions and such that there is nothing to add. In this paper we generalize our previous results in the case of level 2 knowledge spaces and deterministic operators to the case of omega-level knowledge spaces and of non-deterministic operators.