Consistent identification

20 Dezembro 2013, 14:30 José Félix Gomes da Costa

We first proved Smullyan's k-ary recursion theorem (used in vacillatory set identification).


Consistent scientists (for sets).

That consistent scientists TxtEx-identify only classes of recursive sets.

That [TxtEx]cons \subset [TxtEx].

That there are TxtEx-identifiable recursive classes of sets that are not TxtEx-identifiable by consistent scientists.



Diverse classes of Popperian scientists

16 Dezembro 2013, 10:30 José Félix Gomes da Costa


Counting anomalies and mind changes: classes Ex^a_b.

(Case, Jain and Ngo Manguelle) Popperian scientists: classes P_C Ex^a_b and P_C Bc^a_b; classes P*_C Ex^a_b and P*_C Bc^a_b; classes P_T Ex^a_b and P_T Bc^a_b; classes P_R Ex^a_b and P_R Bc^a_b.

Quasi-Popperian scientists: classes TEx^a_b.

That S \in PEX if and only if there exists a recursively enumerable class S' \subseteq R such that S \subseteq S'.

(Barzdins, Blum and Blum) NV-identification and reliable machines. Classes NV and R_C Ex^a_b.

That NV = P_T Ex.


Problem sets

13 Dezembro 2013, 14:30 José Félix Gomes da Costa

We discussed two questions appearing in the set problems:

That Fex* = Ex* (namely the condition to cancel indexes that originate in linear time a number of commission errors greater than the number of occurrences of those indexes along the text.

The operator that allows to separate Bc^{n+1} from Bc^{n}.


Vacillatory identification of sets

9 Dezembro 2013, 10:30 José Félix Gomes da Costa

Vacillatory TxtFex^a_b-identification (a \in N \cup {*} and b \in N). Classes TxtFex^a_ b.

(Case) That TxtFex^0_ {n+1}  -  TxtFex*_n =\= \emptyset  and  TxtFex^{n+1}_ 1  -  TxtFex^n_* =\= \emptyset (and other limit cases). That vacillatory identification improves inductive infering power in set identification.

The class Mex (Freivalds). Mex and Occam's razor argument in the philosophy of science.

(Kimber) That the set S of characteristics of finite sets can not be identified by ''Occam's argument'', i.e., S \in (Mex - Ex). Finite injury priority method.


Popperian scientists

6 Dezembro 2013, 14:30 José Félix Gomes da Costa

This lecture has been replaced by a talk given by the students on Popperian scientists at the CFCUL (Center for the Philosophy of Science, Lisbon University).