This paper introduces a cut-elimination procedure of the intuitionistic sequent calculus and shows that it is isomorphic to the proof reduction of the intuitionistic natural deduction with general elimination and explicit substitution. It also proves strong normalization and Church-Rosser property of the cut-elimination procedure by projecting the sequent calculus to the natural deduction with ...

Nonmonotonic reasoning is succesfully formalized by the class of default logics. In this paper we introduce an axiomatic system for credulous reasoning in rational default logic. Based on classical sequent calculus and anti-sequent calculus, an abstract characterization of credulous nonmonotonic default inference in this variant of default logic is presented.

We present new proofs of cut elimination for intuitionistic, classical, and linear sequent calculi. In all cases the proofs proceed by three nested structural inductions, avoiding the explicit use of multi-sets and termination measures on sequent derivations. This makes them amenable to elegant and concise implementations in Elf, a constraint logic programming language based on the LF logical f...

A sequent calculus for skeptical consequence in infinite autoepistemic theories is presented and proved sound and complete. While skeptical consequence is decidable in the finite case, the move to infinite theories increases the complexity of skeptical reasoning to being Π1-complete. This implies the need for sequent rules with countably many premises, and such rules are employed.

This is an introduction to proof theory of nonclassical logic, which is directed at people who have just started the study of nonclassical logics, using proof-theoretic methods. In our paper, we will discuss only its proof theory based on sequent calculi. So, we will discuss mainly cut elimination and its consequences. As this is not an introduction to sequent systems themselves, we will assume...

We consider two sequent calculi for tense logic in which the syntactic judgements are nested sequents, i.e., a tree of traditional onesided sequents built from multisets of formulae. Our first calculus SKt is a variant of Kashima’s calculus for Kt, which can also be seen as a display calculus, and uses “shallow” inference whereby inference rules are only applied to the top-level nodes in the ne...