29 citations · 39 across the 11 of their papers we have counts for
12 papers
Cyclic proofs in the equational version of Primitive recursive arithmetic
Daniyar Shamkanov
In this brief note, we present a cyclic proof system developed specifically for the equational version of Primitive recursive arithmetic and establish the equivalence of the two sy…
(Non-)well-founded derivations in the provability logic
Daniyar Shamkanov
We examine cyclic, non-well-founded and well-founded derivations in the provability logic . While allowing cyclic derivations does not change the system, the non-well…
Fragments of arithmetic and cyclic proofs
Lev D. Beklemishev, Daniyar S. Shamkanov, Ivan N. Smirnov
We present an alternative cyclic proof system for Peano arithmetic that could be simpler than the existing ones and well-adapted both for proof analysis and for automatizing induct…
A realization theorem for the modal logic of transitive closure
Daniyar Shamkanov
We present a justification logic corresponding to the modal logic of transitive closure and establish a normal realization theorem relating these two systems. The re…
On structural proof theory of the modal logic K+ extended with infinitary derivations
Daniyar Shamkanov
We consider an extension of the modal logic of transitive closure K+ with some inifinitary derivations and present a sequent calculus for this extension, which allows non-well-foun…
On algebraic and topological semantics of the modal logic of common knowledge S4CI
Daniyar Shamkanov
We investigate algebraic and topological semantics of the modal logic S4CI and obtain strong completeness of the given system in the case of local semantic consequence relations. I…
Cut Elimination for Weak Modal Grzegorczyk Logic via Non-Well-Founded Proofs
Yury Savateev, Daniyar Shamkanov
We present a sequent calculus for the weak Grzegorczyk logic Go allowing non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elim…
Non-Well-Founded Proofs for the Grzegorczyk Modal Logic
Yury Savateev, Daniyar Shamkanov
We present a sequent calculus for the Grzegorczyk modal logic Grz allowing cyclic and other non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a…
Cut-elimination for the modal Grzegorczyk logic via non-well-founded proofs
Yury Savateev, Daniyar Shamkanov
We present a sequent calculus for the modal Grzegorczyk logic Grz allowing non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-el…
Some abstract versions of Gödel's second incompleteness theorem based on non-classical logics
Lev Beklemishev, Daniyar Shamkanov
We study abstract versions of Gödel's second incompleteness theorem and formulate generalizations of Löb's derivability conditions that work for logics weaker than the classical on…
Nested Sequents for Provability Logic GLP
Daniyar Shamkanov
We present a proof system for the provability logic GLP in the formalism of nested sequents and prove the cut elimination theorem for it. As an application, we obtain the reduction…
Circular Proofs for Gödel-Löb Logic
Daniyar Shamkanov
We present a sequent-style proof system for provability logic GL that admits so-called circular proofs. For these proofs, the graph underlying a proof is not a finite tree but is a…