ES EL PSICOLOGISMO REFUTABLE SEGÚN FREGE?

Frege Systems

Refutable Inductive Inference of Recursive Functions

Learning of recursive functions refutably informally means that for every recursive function, the learning machine has either to learn this function or to refute it, that is to signal that it is not able to learn it. Three modi of making precise the notion of refuting are considered. We show that the corresponding types of learning refutably are of strictly increasing power, where already the m...

Propositional Proofs in Frege and Extended Frege Systems (Abstract)

We discuss recent results on the propositional proof complexity of Frege proof systems, including some recently discovered quasipolynomial size proofs for the pigeonhole principle and the Kneser-Lovász theorem. These are closely related to formalizability in bounded arithmetic.

The Curse of Frege

I mention two methodological problems with AI's study of inference that have to do with excessive faith in classical logic. The first is the familiar bias toward formalisms that incorporate deductive patterns of argument: a bias against inductive patterns of reasoning. The second is the pretension that inference can be studied with no regard for one's habits of representation. By implicating Fr...

Universes over Frege structures

We investigate universes axiomatized as sets with natural closure conditions over Frege structures. In the presence of a natural form of induction, we obtain a theory of proof-theoretic strength 0 .