The notion of formal proof is defined by finite sequences ($<\omega$ - sequences) of sentences. In some sense if a sentence $\sigma$ is (finitely) provable from the theory $T$ it is very "near" to ...
I am puzzling with the question which of the two proof systems (Hilbert style axiomatic proofs or substructural Sequent Calculi) is the most discriminatory? With discriminatory I mean is which proof ...
Say a proof for the consistency of a formal system (proved within the formal system) is known. There are two possible cases: 1. the formal system is consistent and it can be and has been proven to be, ...
In Gentzen's sequent calculus, a formal proof is described by a tree, with each node representing the sequent obtained from the child(ren) by applying a given inference rule. If no inference rule has ...
Assume you have some notion of proof complexity: for instance, at the basic level, the length of a proof, or the number of symbols used, take your pick (there are more involved measures, but for sake ...
Technically, it is possible to prove anything in Coq proof assistant  (on at least Linux) due to a programming feature (or bug). This seems tractable when validating large proofs. Human analysis ...