arXiv subjects

Kai Bruennler

Publications and source records attributed to Kai Bruennler.

2 recordsLinked to original sources

arXiv2003

Locality for Classical Logic

In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. In addition, they enjoy a top-down symmetry and some normal forms for derivations that are not available in the sequent calculus. Identity axiom, cut, weakening and also contraction can be reduced to atomic form. This leads to rules that are local: they do not require the inspection of expressions of unbounded size.

math.LO↗

arXiv2002

Consistency Without Cut Elimination

In this note we will show how to get consistency for first order classical logic, in a purely syntactic way, without going through cut elimination. The procedure is very simple and it uses the calculus of structures in an essential way. It also shows how finitaryness (in the sense of finite choice of premises for each rule) is actually a triviality (contrarily to what one would guess from textbooks).

math.LO↗