Affiliations: [a] Computer Science Department, Università di Torino, Corso Svizzera 185, 10149 Torino, Italy. [email protected] | [b] Computer Science Department, Università di Torino, Corso Svizzera 185, 10149 Torino, Italy. [email protected]
Note: [*] Address for correspondence: Corso Svizzera 185, 10149 Torino, Italy This author was partially supported by PRIN “Metodi logici per il trattamento dell’informazione”, Anno 2010-2011 - prot. 2010FP79LR_007
Note: [†] This author was partially supported by ICT COST Action IC1201 BETTY, MIUR PRIN Project CINA Prot. 2010LHT4KM and Torino University/Compagnia San Paolo Project SALT.
Abstract: We consider the problem of finding pre-fix 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 answers and possibly forcing us to remove some: in the learning process states of knowledge change non-monotonically. Existence of a pre-fix 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 ω-level knowledge spaces and of non-deterministic operators.
