Research and Publications

My academic interests are logical calculi, proof theory, mathematical logic, complexity theory, cellular automata, combinatorics, and the philosophy of mathematics, but I am also interested in algorithmic art, graphics, and visualizations. My PhD thesis is about sequent calculi for first-order logics with free variables.

The focus of my research has been a method called variable splitting. This is a method applicable to free-variable tableaux, free-variable sequent calculi, connection methods, and matrix characterizations, that reduces redundancies in the search space by exploiting a relationship between branching formulas and universal formulas. Using contextual information to differentiate between occurrences of free variables, the method can be used to assigne different values to these occurrences in a consistent way. Read more in my PhD Thesis.

Publications

Steve Paulson, Barbara J. Grosz, Roger Antonsen
@article{PaulsonGroszAntonsen19,
  author =       {Steve Paulson and Barbara J. Grosz and Roger Antonsen},
  title =        {Human cognition and the {AI} revolution},
  journal =      {Annals of the {N}ew {Y}ork {A}cademy of {S}ciences},
  volume =       0,
  number =       0,
  keywords =     {reality, human cognition, artificial intelligence, AI, computers, mathematics, Turing test, bias},
  doi =          {10.1111/nyas.14122},
  url =          {https://nyaspubs.onlinelibrary.wiley.com/doi/abs/10.1111/nyas.14122},
  eprint =
                  {https://nyaspubs.onlinelibrary.wiley.com/doi/pdf/10.1111/nyas.14122},
  abstract =     {Discovering the true nature of reality may ultimately hinge on grasping the nature and essence of human understanding. What are the fundamental elements or building blocks of human cognition? And how will the rise of superintelligent machines challenge our ideas about cognition, reality, and the limits of human understanding? Logician/mathematician Roger Antonsen and computer science pioneer Barbara J. Grosz join forces to shed light on these questions and the horizon of artificial intelligence.},
}
Roger Antonsen
@inproceedings{Antonsen18,
  author      = {Roger Antonsen},
  title       = {Card Shuffling Visualizations},
  pages       = {451--454},
  booktitle   = {Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture},
  year        = {2018},
  editor      = {Eve Torrence, Bruce Torrence, Carlo S\'equin, and Krist\'of Fenyvesi},
  isbn        = {978-1-938664-27-4},
  issn        = {1099-6702},
  publisher   = {Tessellations Publishing},
  address     = {Phoenix, Arizona},
  note        = {Available online at \url{http://archive.bridgesmathart.org/2018/bridges2018-451.pdf}}
}
Roger Antonsen, Andreas Nakkerud
@article{AntonsenNakkerud18,
  author =       {Roger Antonsen and Andreas Nakkerud},
  title =        {Book Review: Jan von Plato, Elements of Logical Reasoning},
  journal =      {Studia Logica},
  year =         2018,
  month =        February,
  volume =       106,
  number =       1,
  pages =        {215--218},
  issn =         {0039-3215},
  url =          {https://doi.org/10.1007/s11225-018-9783-y},
  doi =          {10.1007/s11225-018-9783-y},
  publisher =    {Springer Netherlands},
}
Christian Mahesh Hansen, Roger Antonsen, Martin Giese, Arild Waaler
@article{HansenAntonsenGieseWaaler12,
  author =    {Christian Mahesh Hansen and Roger Antonsen Martin Giese and Arild Waaler},
  title =     {Incremental {V}ariable {S}plitting},
  journal =   {Journal of {S}ymbolic {C}omputation},
  volume =    47,
  number =    9,
  pages =     {1046–1065},
  year =      2012,
  publisher = {Springer-Verlag},
  ee =        {http://dx.doi.org/10.1016/j.jsc.2011.12.032}
}
Roger Antonsen
@PhdThesis{Antonsen08,
  author =   {Roger Antonsen},
  title =    {The {M}ethod of {V}ariable {S}plitting},
  school =   {University of Oslo},
  year =     2008,
  key =      {Automated Reasoning, Logic, Proof Theory, Connection Method, Tableau Calculus},
  address =  {Department of Informatics},
  month =    {June}
}
Christian Mahesh Hansen, Roger Antonsen, Arild Waaler
@InProceedings{HansenAntonsenWaaler07,
  author =    {Christian Mahesh Hansen and Roger Antonsen and Arild Waaler},
  title =     {Incremental {C}losure of {V}ariable {S}plitting {T}ableaux},
  year =      2007,
  booktitle = {TABLEAUX '07, Automated Reasoning with Analytic Tableaux and Related Methods, Position Papers},
  editor =    {Nicola Olivetti and Camilla Schwind},
  pages =     {65–78},
  publisher = {LSIS},
  volume =    {LSIS.RR.2007.002}
}
Roger Antonsen, Arild Waaler
@InProceedings{AntonsenWaaler07b,
  author =    {Roger Antonsen and Arild Waaler},
  editor =    {Frank Pfenning},
  title =     {A {L}abelled {S}ystem for {IPL} with {V}ariable {S}plitting},
  booktitle = {CADE-21, 21th International Conference on Automated Deduction, Bremen, Germany},
  volume =    4603,
  series =    {Lecture Notes in Computer Science},
  publisher = {Springer-Verlag},
  year =      {2007},
  isbn =      {978-3-540-73594-6},
  pages =     {132–146},
  ee =        {http://dx.doi.org/10.1007/978-3-540-73595-3_10}
}
Roger Antonsen and Arild Waaler
@ARTICLE{AntonsenWaaler07,
  author =   {Roger Antonsen and Arild Waaler},
  title =    {Liberalized {V}ariable {S}plitting},
  journal =  {Journal of Automated Reasoning},
  year =     {2007},
  number =   {1–3},
  volume =   38,
  ee =       {http://dx.doi.org/10.1007/s10817-006-9055-9},
  pages =    {3–30}
}
Roger Antonsen and Arild Waaler
@InProceedings{AntonsenWaaler05,
  author =    {Roger Antonsen and Arild Waaler},
  title =     {Consistency of {V}ariable {S}plitting in {F}ree {V}ariable {S}ystems of {F}irst-{O}rder {L}ogic},
  booktitle = {Automated Reasoning with Analytic Tableaux and Related Methods: 14th International Conference, TABLEAUX, Koblenz, Germany},
  year =      2005,
  pages =     {33–47},
  series =    {Lecture Notes in Computer Science},
  editor =    {Bernhard Beckert},
  volume =    3702,
  isbn =      {3-540-28931-3},
  publisher = {Springer-Verlag},
  ee        = {http://dx.doi.org/10.1007/11554554_5}
}
Roger Antonsen
@InProceedings{Antonsen04,
  author =    {Roger Antonsen},
  title =     {Uniform {V}ariable {S}plitting},
  year =      2004,
  booktitle = {Contributions to the Doctoral Programme of the Second International Joint Conference on Automated Reasoning (IJCAR 2004), Cork, Ireland, 04 July – 08 July, 2004},
  volume =    106,
  publisher = CEUR Workshop Proceedings},
  pages =     {1–5},
  issn =      {1613–0073},
  ee =        {http://ceur-ws.org/Vol-106/01-antonsen.pdf}
}
Arild Waaler and Roger Antonsen
@InProceedings{WaalerAntonsen03,
  author =    {Arild Waaler and Roger Antonsen},
  title =     {A {F}ree {V}ariable {S}equent {C}alculus with {U}niform {V}ariable {S}plitting},
  booktitle = {Automated Reasoning with Analytic Tableaux and Related Methods: International Conference, TABLEAUX, Rome, Italy},
  year =      2003,
  pages =     {214–229},
  series =    {Lecture Notes in Computer Science},
  number =    2796,
  publisher = {Springer-Verlag},
  ee        = {http://dx.doi.org/10.1007/978-3-540-45206-5_17}
}
Roger Antonsen
@mastersthesis{Antonsen03,
  author =   {Roger Antonsen},
  title =    {Free {V}ariable {S}equent {C}alculi},
  year =     2003,
  month =    {May},
  address =  {Language, Logic and Information, Department of Linguistics},
  school =   {University of Oslo},
  publisher = {University of Oslo}
}

Talks

Some research-related talks.

 February 14, 2014 at 12:15
Deterministic Chaos and Cellular Automata
Forum for Mathematical Pearls (and Rarities), NTNU, Trondheim
 November 16, 2011 at 15:50
Closing Show
Forskning.no Conference 2011
 October 29, 2009 at 14:15
RETE
Logic Seminar, Department of Informatics, University of Oslo
 August 9, 2008 at 15:15
The Method of Variable Splitting
Proof, Computation, Complexity -- Intl. Workshop, Oslo, 2008
 January 18, 2008 at 10:15
Variable Splitting for Automated Reasoning
Logic Seminar, University of Oslo
 November 7, 2007
Automated Reasoning
English for Academic Purposes, University of Oslo
 July 17, 2007
A Labelled System for IPL with Variable Splitting
CADE-21 2007, Bremen, Germany
 January 17, 2007
The Theory of Liberalized Variable Splitting
Alta Logic and Computation Workshop, Alta
 March 28, 2006
Variable Splitting: Consistency and Complexity
Seminar in Computing
 February 2, 2006
Variable Splitting: Consistency and Complexity
Seminar in Mathematical Logic
 January 31, 2006
Variable Splitting: Consistency and Complexity
INF5170 - Master Seminar in Logic
 September 16, 2005
Consistency of Variable Splitting in the Free Variable Systems of First-Order Logic
TABLEAUX 2005, Koblenz, Germany
 June 9, 2005
Uniform Variable Splitting
4th Key Symposium 2005, Løkeberg, Sweden
 April 14, 2005
Run-time Skolemization, and Variable Splitting
Seminar in Mathematical Logic
 April 11, 2005
Delta Rules, Skolemization, and Soundness
INF5170 - Master Seminar in Logic
 March 7, 2005
Delta Rules, Skolemization, and Soundness
INF5170 - Master Seminar in Logic
 October 25, 2004
Introduction to Lattice and Order
INF5170 - Master Seminar in Logic, a review of the book "Introduction to Lattice and Order", Davey & Priestley
 July 4, 2004
Uniform Variable Splitting
IJCAR 2004 Doctoral Programme, University College Cork, Cork, Ireland
 September 26, 2003
Proof Search and Free Variable Sequent Calculi
Seminar in Computing, Department of Informatics, University of Oslo
 September 11, 2003
A Free Variable Sequent Calculus with Uniform Variable Splitting
TABLEAUX 2003, Rome, Italy
 June 5, 2003
A Free Variable Calculus with Variable Splitting
Seminar in Mathematical Logic
 February 8, 2001
Introduction To Intuitionistic Logic
Postgraduate Seminar in Logic by language, logic, and information, University of Oslo