Frege: Una estipulación viable

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.

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 .

Truth in Frege

Tarski is widely regarded as the father of formal semantics, and rightly so. But if Tarski is the father, then Frege is the grandfather. Frege’s Grundgesetze der Arithmetik contains a semantic theory for his formal language, his begriffsschrift (or ‘conceptual notation’), that is no less rigorous than the one for the calculus of classes that Tarski develops in the early parts of “The Concept of...