Recently a new connection between proof theory and formal language theory was introduced. It was shown that the operation of cut elimination for proofs in first-order predicate logic involving Π1-cuts corresponds to computing the language of a particular class of regular tree grammars. The present paper expands this connection to the level of Π2-cuts. Given a proof π of a Σ1 formula with cuts o...

Introduction: Aphasia is a language disorder resulting from a lesion in the cerebral cortex. In this case report, we present a polyglot patient who recovered from aphasia by speaking his newly active learned language Case Report: A 69 years old male referred with acute onset right hemiparesis and global aphasia. After imaging, he treated with 75 mg r-TPA (0.9 mg/kg). After the fourth day of ...

We consider the problem of simultaneously compressing a finite set of words by a single grammar. The central result of this paper is the construction of an incompressible sequence of finite word languages. This result is then shown to transfer to tree languages and (via a previously established connection between proof theory and formal language theory) also to formal proofs in first-order pred...