Frege Encore une Fois?

Frege Systems

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.

Interactive Construction of EnCOrE

One of the major challenges of current ITS research is scaling up to real world learning scenarios. Another one, strictly interwoven, is to integrate human learning with other human activities, such as constructing theories or performing experiments, as it is the case in e-Science. The paper describes the results of the first phase of an ambitious project: EnCOrE for building and using an Encyc...

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 .