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Karol Pak

Orcid: 0000-0002-7099-1669

According to our database1, Karol Pak authored at least 69 papers between 2008 and 2023.

Collaborative distances:
  • Dijkstra number2 of four.
  • Erdős number3 of four.

Timeline

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Links

On csauthors.net:

Bibliography

2023
Combining Higher-Order Logic with Set Theory Formalizations.
[BibTeX]
[DOI]
Cezary Kaliszyk
,
Karol Pak
J. Autom. Reason., June, 2023

2022
Prime Representing Polynomial with 10 Unknowns.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., December, 2022

Prime Representing Polynomial with 10 Unknowns - Introduction. Part II.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., December, 2022

Prime Representing Polynomial with 10 Unknowns - Introduction.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2022

Formalizing a Diophantine Representation of the Set of Prime Numbers.
[BibTeX]
[DOI]
Karol Pak
,
Cezary Kaliszyk
Proceedings of the 13th International Conference on Interactive Theorem Proving, 2022

2021
Prime Representing Polynomial.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2021

Formalization of Prime Representing Polynomial in Mizar (short paper).
[BibTeX]
[DOI]
Karol Pak
Proceedings of the Joint Proceedings of the FMM, FVPS, MathUI,NatFoM, and OpenMath Workshops, Doctoral Program, and Work in Progress at the Conference on Intelligent Computer Mathematics 2021 co-located with the 14th Conference on Intelligent Computer Mathematics (CICM 2021), Virtual Event, Timisoara, Romania, July 26, 2021

2020
Grothendieck Universes.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2020

2019
Semantics of Mizar as an Isabelle Object Logic.
[BibTeX]
[DOI]
Cezary Kaliszyk
,
Karol Pak
J. Autom. Reason., 2019

Formalization of the MRDP Theorem in the Mizar System.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2019

Diophantine Sets. Part II.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2019

AIM Loops and the AIM Conjecture.
[BibTeX]
[DOI]
Chad E. Brown
,
Karol Pak
Formaliz. Math., 2019

A Tale of Two Set Theories.
[BibTeX]
[DOI]
Chad E. Brown
,
Karol Pak
Proceedings of the Intelligent Computer Mathematics - 12th International Conference, 2019

Declarative Proof Translation (Short Paper).
[BibTeX]
[DOI]
Cezary Kaliszyk
,
Karol Pak
Proceedings of the 10th International Conference on Interactive Theorem Proving, 2019

Higher-Order Tarski Grothendieck as a Foundation for Formal Proof.
[BibTeX]
[DOI]
Chad E. Brown
,
Cezary Kaliszyk
,
Karol Pak
Proceedings of the 10th International Conference on Interactive Theorem Proving, 2019

2018
The Role of the Mizar Mathematical Library for Interactive Proof Development in Mizar.
[BibTeX]
[DOI]
Grzegorz Bancerek
,
Czeslaw Bylinski
,
Adam Grabowski
,
Artur Kornilowicz
,
Roman Matuszewski
,
Adam Naumowicz
,
Karol Pak
J. Autom. Reason., 2018

Diophantine sets. Preliminaries.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2018

Basic Diophantine Relations.
[BibTeX]
[DOI]
Marcin Acewicz
,
Karol Pak
Formaliz. Math., 2018

Progress in the Formalization of Matiyasevich's Theorem in the Mizar System.
[BibTeX]
[DOI]
Karol Pak
Proceedings of the Joint Proceedings of the CME-EI, 2018

Isabelle Import Infrastructure for the Mizar Mathematical Library.
[BibTeX]
[DOI]
Cezary Kaliszyk
,
Karol Pak
Proceedings of the Intelligent Computer Mathematics - 11th International Conference, 2018

Mizar Set Comprehension in Isabelle Framework.
[BibTeX]
[DOI]
Karol Pak
Proceedings of the Communication Papers of the 2018 Federated Conference on Computer Science and Information Systems, 2018

Combining the Syntactic and Semantic Representations of Mizar Proofs.
[BibTeX]
[DOI]
Karol Pak
Proceedings of the 2018 Federated Conference on Computer Science and Information Systems, 2018

2017
Basel Problem.
[BibTeX]
[DOI]
Karol Pak
,
Artur Kornilowicz
Formaliz. Math., 2017

The Matiyasevich Theorem. Preliminaries.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2017

Basel Problem - Preliminaries.
[BibTeX]
[DOI]
Artur Kornilowicz
,
Karol Pak
Formaliz. Math., 2017

Vieta's Formula about the Sum of Roots of Polynomials.
[BibTeX]
[DOI]
Artur Kornilowicz
,
Karol Pak
Formaliz. Math., 2017

Pell's Equation.
[BibTeX]
[DOI]
Marcin Acewicz
,
Karol Pak
Formaliz. Math., 2017

Presentation and Manipulation of Mizar Properties in an Isabelle Object Logic.
[BibTeX]
[DOI]
Cezary Kaliszyk
,
Karol Pak
Proceedings of the Intelligent Computer Mathematics - 10th International Conference, 2017

Isabelle Formalization of Set Theoretic Structures and Set Comprehensions.
[BibTeX]
[DOI]
Cezary Kaliszyk
,
Karol Pak
Proceedings of the Mathematical Aspects of Computer and Information Sciences, 2017

Progress in the Independent Certification of Mizar Mathematical Library in Isabelle.
[BibTeX]
[DOI]
Cezary Kaliszyk
,
Karol Pak
Proceedings of the 2017 Federated Conference on Computer Science and Information Systems, 2017

Formalization of Pell's Equations in the Mizar System.
[BibTeX]
[DOI]
Marcin Acewicz
,
Karol Pak
Proceedings of the 2017 Federated Conference on Computer Science and Information Systems, 2017

2016
Leibniz Series for π.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2016

Towards a mizar environment for isabelle: foundations and language.
[BibTeX]
[DOI]
Cezary Kaliszyk
,
Karol Pak
,
Josef Urban
Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs, 2016

The impact of proof steps sequence on proof readability - experimental setting.
[BibTeX]
[DOI]
Karol Pak
,
Aleksy Schubert
Proceedings of the Joint Proceedings of the FM4M, 2016

Lemma Extraction Criteria Based on Properties of Theorem Statements.
[BibTeX]
[DOI]
Karol Pak
Proceedings of the Joint Proceedings of the FM4M, 2016

Topological Foundations for a Formal Theory of Manifolds.
[BibTeX]
[DOI]
Karol Pak
Proceedings of the Joint Proceedings of the FM4M, 2016

2015
Improving Legibility of Formal Proofs Based on the Close Reference Principle is NP-Hard.
[BibTeX]
[DOI]
Karol Pak
J. Autom. Reason., 2015

Euler's Partition Theorem.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2015

Flexary Operations.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2015

Readable Formalization of Euler's Partition Theorem in Mizar.
[BibTeX]
[DOI]
Karol Pak
Proceedings of the Intelligent Computer Mathematics - International Conference, 2015

Mizar: State-of-the-art and Beyond.
[BibTeX]
[DOI]
Grzegorz Bancerek
,
Czeslaw Bylinski
,
Adam Grabowski
,
Artur Kornilowicz
,
Roman Matuszewski
,
Adam Naumowicz
,
Karol Pak
,
Josef Urban
Proceedings of the Intelligent Computer Mathematics - International Conference, 2015

2014
Topological Manifolds.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2014

Bertrand's Ballot Theorem.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2014

Brouwer Invariance of Domain Theorem.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2014

Tietze Extension Theorem for n-dimensional Spaces.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2014

Improving legibility of natural deduction proofs is not trivial.
[BibTeX]
[DOI]
Karol Pak
Log. Methods Comput. Sci., 2014

Automated Improving of Proof Legibility in the Mizar System.
[BibTeX]
[DOI]
Karol Pak
Proceedings of the Intelligent Computer Mathematics - International Conference, 2014

2013
Methods of Lemma Extraction in Natural Deduction Proofs.
[BibTeX]
[DOI]
Karol Pak
J. Autom. Reason., 2013

2012
The Friendship Theorem.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2012

The Rotation Group.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2012

Trust in RDF Graphs.
[BibTeX]
[DOI]
Dominik Tomaszuk
,
Karol Pak
,
Henryk Rybinski
Proceedings of the Advances in Databases and Information Systems, 2012

2011
Brouwer Fixed Point Theorem in the General Case.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2011

Brouwer Fixed Point Theorem for Simplexes.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2011

Continuity of Barycentric Coordinates in Euclidean Topological Spaces.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2011

Linear Transformations of Euclidean Topological Spaces. Part II.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2011

Linear Transformations of Euclidean Topological Spaces.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2011

2010
Sperner's Lemma.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2010

The Geometric Interior in Real Linear Spaces.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2010

Abstract Simplicial Complexes.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2010

Affine Independence in Vector Spaces.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2010

2009
Small Inductive Dimension of Topological Spaces. Part II.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2009

Small Inductive Dimension of Topological Spaces.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2009

Basic Properties of Metrizable Topological Spaces.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2009

2008
Jordan Matrix Decomposition.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2008

Eigenvalues of a Linear Transformation.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2008

Linear Map of Matrices.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2008

Block Diagonal Matrices.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2008

Solutions of Linear Equations.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2008

Complete Spaces.
[BibTeX]
[DOI]
Karol Pak
Formaliz. Math., 2008


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