Asta (formerly Andreas) Halkjær
From
I am a PhD student at DTU Compute since February 2020 working on Formally Correct Deduction Methods for Computational Logic, especially using the proof assistant Isabelle/HOL. My supervisor is Jørgen Villadsen and my cosupervisor is Nina Gierasimczuk.
I was a MSc student on the Honours Programme in Computer Science and Engineering at DTU from 2018 to 2020. My MSc thesis on Hybrid Logic was supervised by Jørgen Villadsen, Alexander Birch Jensen and Patrick Blackburn.
Academic Activities
 Cochair of the Logic and Computation track for the Student Session @ 32nd European Summer School in Logic, Language and Information (ESSLLI 2021).
Articles

Interactive Theorem Proving for Logic and Information in
Natural Language Processing
in Artificial Intelligence — NLPinAI 2021
Jørgen Villadsen, Asta Halkjær From, Alexander Birch Jensen, Anders Schlichtkrull.
DOI: 10.1007/9783030901387_2
Formalizations: Epistemic Logic, Public Announcement Logic 
Formalized Soundness and Completeness of Epistemic Logic at
WoLLIC 2021
Asta Halkjær From.
DOI: 10.1007/9783030888534_1
Formalization: Epistemic Logic 
A Sequent Calculus for FirstOrder Logic Formalized in Isabelle/HOL at
CILC 2021
Asta Halkjær From, Anders Schlichtkrull, Jørgen Villadsen.
CEURWS: PDF
Formalization: Sequent Calculus  A Case Study in ComputerAssisted Metareasoning at DCAI 2021, Special Session on Computational Linguistics, Information, Reasoning, and AI (CompLingInfoReasAI'21) Asta Halkjær From, Simon Tobias Lund, Jørgen Villadsen.
 Formalizing Axiomatic Systems for Propositional Logic in Isabelle/HOL at Conference on Intelligent Computer Mathematics (CICM 2021) Asta Halkjær From, Agnes Moesgård Eschen, Jørgen Villadsen.
 Teaching Automated Reasoning and Formally Verified Functional Programming in Agda and Isabelle/HOL at 10th International Workshop on Trends in Functional Programming in Education (TFPIE 2021) Asta Halkjær From, Jørgen Villadsen.

Synthetic Completeness for a Terminating SeligmanStyle Tableau System in
TYPES 2020 postproceedings
Asta Halkjær From.
DOI: 10.4230/LIPIcs.TYPES.2020.5
Formalization: Hybrid Logic 
Isabelle/HOL as a MetaLanguage for Teaching Logic in
ThEdu'20 postproceedings
Asta Halkjær From, Jørgen Villadsen, Patrick Blackburn.
DOI: 10.4204/EPTCS.328.2

Hybrid Logic in the Isabelle Proof Assistant: Benefits, Challenges and the Road Ahead
(short paper) at AiML 2020
Asta Halkjær From
Booklet: PDF
Formalization: Hybrid Logic 
Formalizing HenkinStyle Completeness of an Axiomatic System for Propositional
Logic
at WeSSLLII + ESSLLI Virtual Student Session 2020 Asta Halkjær FromProceedings: PDF

A Concise Sequent Calculus for Teaching FirstOrder Logic at
Isabelle Workshop 2020
Asta Halkjær From, Jørgen Villadsen.
Paper: PDF

Formalizing a SeligmanStyle Tableau System for Hybrid Logic (short paper) at
IJCAR 2020
Asta Halkjær From, Patrick Blackburn, Jørgen Villadsen.
DOI: 10.1007/9783030510749_27
Formalization: Hybrid Logic 
Teaching a Formalized Logical Calculus in
ThEdu'19 postproceedings
Asta Halkjær From, Alexander Birch Jensen, Anders Schlichtkrull, Jørgen Villadsen.
DOI: 10.4204/EPTCS.313.5
 MultiAgent Programming Contest 2018  The JasonDTU Team Jørgen Villadsen, Mads Okholm Bjørn, Andreas Halkjær From, Thomas Søren Henney, John Bruntse Larsen.

A Verified Simple Prover for FirstOrder Logic at
PAAR 2018
Jørgen Villadsen, Anders Schlichtkrull, Andreas Halkjær From.
Paper: PDF

Students' Proof Assistant (SPA) in
ThEdu'18 postproceedings
Anders Schlichtkrull, Jørgen Villadsen, Andreas Halkjær From.
DOI: 10.4204/EPTCS.290.1

Natural Deduction Assistant (NaDeA) in
ThEdu'18 postproceedings
Jørgen Villadsen, Andreas Halkjær From, Anders Schlichtkrull.
DOI: 10.4204/EPTCS.290.2

Substitutionless FirstOrder Logic: A Formal Soundness Proof at
Isabelle Workshop 2018
Andreas Halkjær From, John Bruntse Larsen, Anders Schlichtkrull, Jørgen Villadsen.
Paper: PDF

Drawing Trees at
Isabelle Workshop 2018
Andreas Halkjær From, Anders Schlichtkrull, Jørgen Villadsen.
Paper: PDF, Formalization: Isabelle theory

Natural Deduction and the Isabelle Proof Assistant in
ThEdu'17 postproceedings
Jørgen Villadsen, Andreas Halkjær From, Anders Schlichtkrull.
DOI: 10.4204/EPTCS.267.9
 MultiAgent Programming Contest 2016  The PythonDTU Team in IJAOSE 2018 Jørgen Villadsen, Andreas Halkjær From, Salvador Jacobi, Nikolaj Nøkkentved Larsen.

Code Generation for a Simple FirstOrder Prover at
Isabelle Workshop 2016
Jørgen Villadsen, Anders Schlichtkrull, Andreas Halkjær From.
Paper: PDF
Start of PhD
Published formalizations

Soundness and Completeness of an Axiomatic System for FirstOrder Logic in
Archive of Formal Proofs (October 2021)
Asta Halkjær From
This work is a formalization of the soundness and completeness of an axiomatic system for firstorder logic. The proof system is based on System Q1 by Smullyan and the completeness proof follows his textbook "FirstOrder Logic" (SpringerVerlag 1968). The completeness proof is in the Henkin style where a consistent set is extended to a maximal consistent set using Lindenbaum's construction and Henkin witnesses are added during the construction to ensure saturation as well. The resulting set is a Hintikka set which, by the model existence theorem, is satisfiable in the Herbrand universe.

Public Announcement Logic in
Archive of Formal Proofs (June 2021)
Asta Halkjær From
This work is a formalization of public announcement logic with countably many agents. It includes proofs of soundness and completeness for a variant of the axiom system PA + DIST! + NEC!. The completeness proof builds on the Epistemic Logic theory.

Epistemic Logic: Completeness of Modal Logics in
Archive of Formal Proofs (October 2018, updated April
2021)
Asta Halkjær From
This work is a formalization of epistemic logic with countably many agents. It includes proofs of soundness and completeness for the axiom system K. The completeness proof is based on the textbook "Reasoning About Knowledge" by Fagin, Halpern, Moses and Vardi (MIT Press 1995). The extensions of system K (T, KB, K4, S4, S5) and their completeness proofs are based on the textbook "Modal Logic" by Blackburn, de Rijke and Venema (Cambridge University Press 2001).

Hybrid Logic in
Archive of Formal Proofs (December 2019, updated June
2020)
Asta Halkjær From
The formalization accompanying my MSc thesis and TYPES 2020 paper.
This work is a formalization of soundness and completeness proofs for a Seligmanstyle tableau system for hybrid logic. The completeness result is obtained via a synthetic approach using maximally consistent sets of tableau blocks. The formalization differs from previous work in a few ways. First, to avoid the need to backtrack in the construction of a tableau, the formalized system has no unnamed initial segment, and therefore no Name rule. Second, I show that the full Bridge rule is admissible in the system. Third, I start from rules restricted to only extend the branch with new formulas, including only witnessing diamonds that are not already witnessed, and show that the unrestricted rules are admissible. Similarly, I start from simpler versions of the @rules and show that these are sufficient. The GoTo rule is restricted using a notion of potential such that each application consumes potential and potential is earned through applications of the remaining rules. I show that if a branch can be closed then it can be closed starting from a single unit. Finally, Nom is restricted by a fixed set of allowed nominals. The resulting system should be terminating.

A Sequent Calculus for FirstOrder Logic in
Archive of Formal Proofs (July 2019)
Asta Halkjær From
This work formalizes soundness and completeness of a onesided sequent calculus for firstorder logic. The completeness is shown via a translation from a complete semantic tableau calculus, the proof of which is based on the FirstOrder Logic According to Fitting theory. The calculi and proof techniques are taken from BenAri's Mathematical Logic for Computer Science.

IsaFoL: Isabelle Formalization of Logic
I have contributed to a number of formalizations in the IsaFoL project:
Abstracts
 On the Use of Isabelle/HOL for Formalizing New Concise Axiomatic Systems for Classical Propositional Logic at TYPES 2021 Asta Halkjær From and Jørgen Villadsen
 Formalized Soundness and Completeness of Epistemic Logic at LAMAS & SR 2021 Asta Halkjær From, Alexander Birch Jensen and Jørgen Villadsen
 Formalized soundness and completeness of natural deduction for firstorder logic at SLS 2018 Andreas Halkjær From.
 Teaching firstorder logic with the natural deduction assistant (NaDeA) at SLS 2018 Andreas Halkjær From, Helge Hatteland, Jørgen Villadsen.
Theses

MSc: Hybrid Logic (January 2020)
My MSc thesis on formalizing the soundness and completeness of a Seligmanstyle tableau system for hybrid logic in Isabelle/HOL.

BSc: Formalized FirstOrder Logic (July 2017)
My BSc thesis on formalizing the soundness and completeness of NaDeA in Isabelle/HOL.
Talks

Formalized Soundness and Completeness of Epistemic Logic (October 2021)
Given at WoLLIC 2021

Formalizing Axiomatic Systems for Propositional Logic in Isabelle/HOL (July 2021)
Given at CICM 2021

Formalized Soundness and Completeness of Epistemic Logic (May 2021)
Given at LAMAS & SR 2021

Hybrid Logic (January 2021)
Given at 3rd World Logic Day  14 January 2021  A Zoom on Logic.

Belief Revision and Isabelle/HOL (November 2020)
Given at a DTU seminar course.

Hybrid Logic in the Isabelle Proof Assistant: Benefits, Challenges and the Road Ahead
Given at AiML 2020.

Formally Correct Deduction Methods for Computational Logic (July 2020)
Given at CICM 2020 doctoral session.

Formalizing HenkinStyle Completeness of an Axiomatic System for Propositional Logic (July 2020)

Formalizing a SeligmanStyle Tableau System for Hybrid Logic (July 2020)
Overview of our paper. Recording: YouTube. Given at IJCAR 2020.

A Concise Sequent Calculus for Teaching FirstOrder Logic (June 2020)
Overview of our paper. Recording: YouTube. Given at the Isabelle Workshop 2020.

The Isabelle Proof Assistant and Hybrid Logic: Formalizing SeligmanStyle Tableaux (October 2019)
Update on my MSc thesis work. Given at an AlgoLoG seminar at DTU.

Using the Isabelle Proof Assistant: SeligmanStyle Tableau for Hybrid Logic (September 2019)
The Isabelle proof assistant can be used to mechanically develop and check results in logic, mathematics, computer science etc. In this talk I motivate this process and explain how it looks in practice for a basic hybrid logic. The running example will be preliminary work on the completeness and termination for a Seligmanstyle tableau system by Blackburn, Bolander, Braüner and Jørgensen. Given at The LogicS of Prior Past, Present, and Future at Roskilde University.

Magnolia – Implementing System F with Anonymous Sums and Products (March 2018)
Overview of the Complete and Easy Bidirectional Type Checking for HigherRank Polymorphism paper as well as my own additions. Also briefly describes Abstract Binding Trees. Given at DTU.

FIT – From's Isabelle Tutorial – Verification of Quicksort (October 2017)
A fastpaced, handson introduction to Isabelle/HOL I gave at PART DTU.
Work Experience
Teaching Assistant
I have been a TA in the following courses: 02101 Introductory Programming, fall 2015
 02105 Algorithms and Data Structures 1, spring 2016
 02101 Introductory Programming, fall 2016
 02110 Algorithms and Data Structures 2, fall 2016
 02105 Algorithms and Data Structures 1, spring 2017
 02180 Introduction to Artificial Intelligence, spring 2018
 02156 Logical Systems and Logic Programming, fall 2018
 02156 Logical Systems and Logic Programming, fall 2019
 02102 Introductory Programming, spring 2020
 02256 Automated Reasoning, spring 2020
 02287 Logical Theories for Uncertainty and Learning, fall 2020