# Daniyar ShamkanovSteklov Mathematical Institute of RAS · Department of Mathematical Logic

Daniyar Shamkanov

Candidate of physico-mathematical sciences

## About

15

Publications

425

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60

Citations

Introduction

**Skills and Expertise**

Additional affiliations

September 2012 - present

September 2011 - present

**Steklov Mathematical Institute of RAS**

Position

- Research Associate

## Publications

Publications (15)

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. In addition, we consider an extension of the logic S4CI with certain infinitary derivations and establish strong completeness results for the obtained system in the case o...

Non-well-founded derivations in the Gödel-Löb provability logic - Daniyar Shamkanov

We present a sequent calculus for the weak Grzegorczyk logic \(\mathsf {Go}\) allowing non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elimination mapping acting on these proofs.

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 continuous cut-elimination mapping acting on these proofs. As an application, we establish the Lyndon interpolation property for the logic Grz proof-theoretically.

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-elimination mapping acting on these proofs.

The Gödel-Löb provability logic \(\mathsf {GL}\) is strongly neighbourhood complete in the case of the so-called local semantic consequence relation. In the given paper, we consider Hilbert-style non-well-founded derivations in \(\mathsf {GL}\) and establish that \(\mathsf {GL}\) with the obtained derivability relation is strongly neighbourhood com...

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-elimination mapping acting on these proofs.

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 one. We isolate the role of contraction rule in Gödel's theorem and give a (toy) example of a system based on modal logic without contraction invalidating Gödel's argument.

We present a new justification logic corresponding to the Gödel-Löb provability logic GL and prove the realization theorem connecting these two systems in such a way that all the realizations provided in the theorem are normal. © 2016 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.

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 of GLP to its important fragment called J
syntactically.

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 allowed to contain cycles. As an application, we
establish Lyndon interpolation for GL syntactically.

We study interpolation properties of provability logics. We prove the Lyndon interpolation for GL and the uniform interpolation for GLP.

Reflexive combinatory logic RCL was introduced by S. Artemov as an extension of typed combinatory logic CL
→ capable to internalize its own derivations of typing judgments. It was designed as a basic theoretical prototype of functional
programming languages extended by this kind of self-referential capacity. However, its operational aspects remaine...