Fall 2022:
Phil 220: Symbolic Logic 2
Phil 365: Philosophy of computing
Winter 2023:
Phil 367: Introduction to the philosophy of
mathematics
Phil 421/Phil 522: Modal Logic/Topics in
Logic
Other courses
I taught the following philosophy courses (some of them many times) in
the last several years. (These are all “PHIL” courses, listed by
number, in decreasing order.)
 422/522 Topic: Relevance and substructural logics
 422/522 Topic: Computability and Gödel's incompleteness theorems
 422/522 Topic: Gödel's incompleteness theorems
 422/522 Topic: Gaggle theory applied to modal, relevance and other
nonclassical logics
 422/522 Topic: Proof theory of classical and substructural logics
 421/522 Modal Logic/Topics in Logic
 420/522 Metalogic/Topics in Logic
 367 Introduction to the Philosophy of Mathematics
 365 Philosophy of Computing
 325 Risk, Choice and Rationality
 220 Symbolic Logic 2
 120 Symbolic Logic 1

My main research area is logic. I am
especially interested in nonclassical logics, including relevance
and substructural logics, modal logics, combinatory
logic and λcalculuses. Nonclassical
logics were first introduced as a solution to philosophical
problems such as the problem of implication and entailment. Later
on, new logics emerged in other disciplines too — from mathematics to
informatics and linguistics. Some of my research interests —
beyond logic and the philosophy of logic — are connected to the latter
areas. I have a keen interest in the philosophy of mathematics, in
particular, in the foundations of mathematics. I also try to follow
the latest developments in informatics, especially, those that concern
questions related to the theory of computing — like algorithmics,
information theory, complexity theory, programming language design and cyber
security. Earlier, I worked on some questions in the semantics of
natural languages, primarily, using modal (specifically, temporal and tense)
logics and discourse representation theory.
Some of my research results concern semantics for various
nonclassical logics (e.g., calculuses for combinatory logic).
J. Michael Dunn and I wrote a book on
the relational semantics of nonclassical logics. These kinds
of semantics generalize Kripke's possibleworld semantics for normal modal
logics, and have been the preferred sort of semantics for decades.
Some years ago, we worked out representations for Kleene logic and action
logic, which are closely related to dynamic logic. We also
collaborated on defining a “fourvalued” semantics for minimal
substructural logic. Within a SSHRC IG project, we worked on the
history of the threetermed relational semantics and problems of its
applicability to relevance logics with thin sets of connectives.
The (first) Third Workshop, which took
place on May 16–17, 2016, at the University of Alberta
[workshop poster], was thematically connected to
the same SSHRC IG. I continue to work on questions related to various
relational semantics for substructural logics — especially, from
the perspective of Dunn's gaggle theory (i.e., generalized
Galois logics) as part of my SSHRC IG.
A more precise characterization of classes of structures for various
nonclassical logics leads straightforwardly to topological
frames. I proved full topological duality theorems for ortho
and De Morgan lattices and for the algebra of the logic of entailment.
These duality theorems provide plenty of insights into the logics themselves,
because interpretations of formulas can be viewed as maps in a category.
Combinatory logic and λcalculuses are connected to other
nonclassical logics in various ways, one of which is the Curry–Howard
correspondence (CHC). J. Michael Dunn and I wrote a paper about
extracting combinatory inhabitants from proofs in a sequent calculus for
implicational ticket entailment, and I further applied the approach to
implicational intuitionistic logic. The use of sequent calculuses
— instead of a natural deduction system — leads to other
combinator sets and other combinatory inhabitants than usual. This
approach shows a way to extend CHC without switching to λterms or
introducing a substitution operation. Typable combinatory terms
encode proofs in an axiomatic formulation of a logic; therefore, the question
of decidability turns into the question of inhabitation.
Combinatory logic in itself is an elegant and powerful
formalism that can represent computable functions — just as,
for instance, abacus machines can. These are some of the motivations
why I wrote a book on combinatory
logic.
The proof theory of nonclassical logics sometimes gets really
tricky. The original sequent calculuses LK and LJ are
seemingly simple proof systems, but in reality, the proofs are tightly
controlled — as evidenced by the cut theorem. Some wellknown
relevance logics cannot be formalized as extensions of the associative Lambek
calculus, which causes various “technical complications.”
I succeeded in defining sequent calculuses for some of these relevance logics
— including E^{t}_{+} — together
with proving the cut theorem for them. A major research project that
I and J. Michael Dunn worked on (as a SSHRC SRG), was the problem of
the decidability of the implicational fragment of ticket entailment,
which remained open for over 50 years. Our decidability proof was made
possible by a new sequent calculus for implicational
R^{t} (R^{t}_{→}), which extends a
sequent calculus for implicational T^{t} by two rules that
add the exact difference between these logics to the latter to obtain the
former. I wrote a book on proof
theory with a focus on sequent calculuses (including some tableaux and
resolution systems).
J. Michael Dunn and I proved the decidability of several modal relevance
logics — including propositional linear logic. I proved some
related results such as the decidability of MELL and that of NLL (in a group
of certain semilattice based modal logics).
Problems with the reception
of our results, which stem from a lack of understanding of sequent calculuses,
led to the introduction of a new research area called reverse
computation, in 2019. One of the first results in reverse
computation is that abacus machines cannot reverse compute primitive recursive
functions.
I am certain that logic — together with its many connections
and offsprings — is an exciting and thriving field of
research, which is of utmost importance for the protection and enhancement
of rationality.

Mailing address:
University of Alberta
Department of Philosophy
243 Assiniboia Hall
Edmonton, AB T6G 2E7, Canada
Email address:
Page updated on:
July 4th, 2022
My Erdös number:
Three (i.e., 3)
Memberships:
Association for Symbolic Logic
(ASL)
American Mathematical Society (AMS)
Society for Exact
Philosophy
(SEP)
American Philosophical Association
(APA)
Friends of the Stanford
Encyclopedia
of Philosophy
Some U of A links:
University of Alberta
Department of Philosophy

 K. Bimbó and J. M. Dunn, “Modalities in latticeR,” in
Relevance Logics and other Tools for Reasoning. Essays in Honor of
J. Michael Dunn, K. Bimbó (ed.), Tributes, vol. 46, College
Publications, London, UK, 2022, pp. 89–127.
 K. Bimbó (ed.), Relevance Logics and other Tools for Reasoning. Essays
in Honor of J. Michael Dunn, Tributes, vol. 46, College Publications,
London, UK, 2022. (The book @ College
Publications. Table of contents (PDF).)
 K. Bimbó and J. M. Dunn, “St. Alasdair on lattices
everywhere,” in Alasdair Urquhart on Nonclassical and Algebraic
Logic, and Complexity of Proofs, I. Düntsch and E. Mares (eds.),
Outstanding Contributions to Logic, vol. 22, Springer Nature,
Switzerland, 2022, pp. 323–346. (The paper
@ Springer Link.)
 K. Bimbó, “Interpretations of weak positive modal logics,”
in Arnon Avron on Semantics and Proof Theory for Nonclassical
Logics, O. Arieli and A. Zamansky (eds.), Outstanding Contributions
to Logic, vol. 21, Springer Nature, Switzerland, 2021,
pp. 13–38. (The paper
@ Springer Link.)
 K. Bimbó, “The development of decidability proofs based on
sequent calculi,” in Contemporary Logic and Computing,
A. Rezuş (ed.), Landscapes in Logic, vol. 1, College Publications,
London (UK), 2020, pp. 5–37. (The
volume
@ College Publications.)
 K. Bimbó, “On the algebraization of relevance logics. (A
preamble to J. Michael Dunn's PhD dissertation),” in Logic
PhDs, vol. 2: J. Michael Dunn, The Algebra of Intensional
Logics, College Publications, London (UK), 2019,
pp. 1–22. (The
volume
@ College Publications.)
 K. Bimbó, “Default rules in the logic of firstdegree
entailments,” in New Essays on Belnap–Dunn Logic,
H. Omori and H. Wansing (eds.), Synthese Library, vol. 418, Springer
Nature, Switzerland, 2019, pp. 113–131. (The paper
@ Springer Link.)
 K. Bimbó, “Inhabitants of intuitionistic implicational
theorems,” in Logic, Language, Information and Computation.
Proceedings of the 25th International Workshop, WoLLIC 2018, Bogota,
Colombia, July 24–27, 2018., L. S. Moss, R. de Queiroz and M.
Martinez (eds.), Lecture Notes in Coputer Science, vol. 10944,
Springer, 2018, pp. 1–24. (The paper
@ Springer Link.)
 K. Bimbó, J. M. Dunn and N. Ferenz, “Two manuscripts, one by
Routley, one by Meyer: The origins of the Routley–Meyer semantics for
relevance logics,” Australasian Journal of Logic 15 (2018),
pp. 171–209. (The paper
@ Victoria University of Wellington.)
 K. Bimbó and J. M. Dunn, “Larisa Maksimova’s early
contributions to relevance logic,” in Larisa Maksimova on
Implication, Interpolation and Definability, S. Odintsov (ed.),
Outstanding Contributions to Logic, vol. 15, Springer Nature,
Switzerland, 2018, pp. 33–60. (The paper
@ Springer Link.)
 K. Bimbó, “On the decidability of certain semilattice based
modal logics,” in Automated Reasoning with Analytic Tableaux and
Related Methods. Proceedings of the 26th International Conference,
TABLEAUX 2017, Brasilia, Brazil, September 25–28, 2017,
R.A. Schmidt and C. Nalon (eds.), Lecture Notes in Artificial
Intelligence, vol. 10501, Springer, 2017, pp. 44–61.
(The
paper @ Springer Link.)
 K. Bimbó and J. M. Dunn (eds.), Proceedings of the
Third Workshop, May 16–17, 2016, Edmonton, Canada, special
issue of the IFCoLog Journal of Logics and their Applications 4(3)
(2017).
 K. Bimbó and J. M. Dunn, “The emergence of settheoretical
semantics for relevance logics around 1970,” in Proceedings of
the Third Workshop, May 16–17, 2016, Edmonton, Canada, K. Bimbó
and J. M. Dunn (eds.), special issue of the IFCoLog Journal of Logics
and their Applications 4 (2017), pp. 557–589.
 K. Bimbó (ed.), J. Michael Dunn on Information Based Logics,
Outstanding Contributions to Logic, vol. 8, Springer International
Publishing AG, Switzerland, 2016. (The book
@ Springer's web site; the book@
Springer Link. Table of contents (PDF).)
 K. Bimbó, “Some relevance logics from the point of view of relational
semantics,” in Israeli Workshop on Nonclassical Logics and their
Applications (IsraLog 2014), O. Arieli and A. Zamansky (eds.),
special issue of the Logic Journal of the IGPL 24 (2016),
pp. 268–287. (The paper @ Oxford University Press.)
 K. Bimbó, “The decidability of the intensional
fragment of classical linear logic,” Theoretical Computer
Science 597 (2015), pp. 1–17. (The
paper @ Elsevier.)
 K. Bimbó, Proof Theory: Sequent Calculi and
Related Formalisms, CRC Press, Boca Raton, FL, 2015.
(The book @
the CRC web site.)
(A growing collection of solutions to selected exercises from
the book and an amendment to the book.)
 K. Bimbó, “Current trends in substructural logics,” in
JPL40: The fortieth anniversary issue of the Journal of Philosophical
Logic, J. Horty and F. Veltman, (eds.), special issue of the
Journal of Philosophical Logic 44 (2015),
pp. 609–624. (The paper
@ Springer Link.)
 K. Bimbó and J. M. Dunn, “Extracting BB'IW
inhabitants of simple types from proofs in the sequent calculus
LT^{t}_{→} for implicational ticket
entailment,” Logica Universalis 8(2) (2014),
pp. 141–164. (The paper
@ Springer Link.)
 K. Bimbó and J. M. Dunn, “On the decidability
of implicational ticket entailment,” Journal of Symbolic
Logic 78(1) (2013), pp. 214–236.
(The paper
@ Cambridge University Press.)
 K. Bimbó and J. M. Dunn, “New consecution
calculi for R^{t}_{→},” Notre Dame
Journal of Formal Logic 53(4) (2012),
pp. 491–509. (The paper @
Project Euclid.)
 K. Bimbó, Combinatory Logic: Pure, Applied and
Typed, CRC Press, Boca Raton, FL, 2012.
(The book
@ the CRC Press web site.)
 K. Bimbó and J. M. Dunn, “Calculi for symmetric generalized Galois
logics,” in A Festschrift for Joachim Lambek, J. van Benthem
and M. Moortgat (eds.), Linguistic Analysis,
36 (2010), pp. 307–343. (The
volume @
Linguistic Analysis.)
 K. Bimbó, “Schönfinkeltype operators for classical logic,”
Studia Logica 95 (2010), pp. 355–378. (The
paper
@ Springer Link.)
 K. Bimbó and J. M. Dunn, “Symmetric generalized Galois
logics,” Logica Universalis 3 (2009),
pp. 125–152. (The paper
@ Springer Link.)
 K. Bimbó, J. M. Dunn and R. D. Maddux, “Relevance logics and
relation algebras,” Review of Symbolic Logic 2 (2009),
pp. 102–131.
(The paper @ CUP.)
 K. Bimbó, “Combinatory
logic,” Stanford Encyclopedia of Philosophy.
 K. Bimbó, “Dual gaggle semantics for entailment,”
Notre Dame Journal of Formal Logic 50 (2009),
pp. 23–41. (The paper @ Project Euclid.)
 K. Bimbó and J. M. Dunn, Generalized Galois
Logics. Relational Semantics of Nonclassical Logical Calculi, CSLI
Lecture Notes, v. 188, CSLI, Stanford, CA, 2008.
(The book
@ CSLI Publications and the book @ the University of Chicago Press.)
 K. Bimbó, “Functorial duality for
ortholattices and De Morgan lattices,” Logica
Universalis 1 (2007), pp. 311–333.
(The paper
@ Springer Link.)
 K. Bimbó, “LE^{t}_{→},
LR^{°}_{ˆ˜}, LK and cut free proofs,”
Journal of Philosophical Logic 36 (2007),
pp. 557–570. (The paper
@ Springer Link.)
 K. Bimbó, “Relevance logics,” in
Philosophy of Logic, D. Jacquette (ed.), (volume 5 of Handbook
of the Philosophy of Science, D. Gabbay, P. Thagard, J. Woods (eds.)),
Elsevier (NorthHolland), 2006, pp. 723–789. (The Handbook
of the Philosophy of Science project and the book @ at Elsevier.)
 K. Bimbó, “Admissibility of cut in LC
with fixed point combinator,” Studia Logica 81 (2005),
pp. 399–423. (The paper
@ Springer Link.)
 K. Bimbó, “The ChurchRosser property in symmetric
combinatory logic,” Journal of Symbolic Logic 70
(2005), pp. 536–556. (The paper
at CUP.)
 K. Bimbó and J. M. Dunn, “Relational semantics
for Kleene logic and action logic,” Notre Dame Journal of
Formal Logic 46 (2005), pp. 461–490.
(The paper
@ Project Euclid.)
 K. Bimbó, “Types of Ifree hereditary right
maximal terms,” Journal of Philosophical Logic 34
(2005), pp. 607–620. (The paper
@ Springer Link.)
 K. Bimbó, “Semantics for dual and symmetric
combinatory calculi,” Journal of Philosophical Logic, 33
(2004), pp. 125–153. (The paper @ Springer Link.)
 K. Bimbó, “The ChurchRosser property in dual combinatory
logic,” Journal of Symbolic Logic 68 (2003),
pp. 132–152. (The paper at CUP.)
 K. Bimbó and J. M. Dunn, “Fourvalued
logic,” Notre Dame Journal of Formal Logic 42 (2002),
pp. 171–192. (The paper @
Project Euclid.)
 K. Bimbó, “Semantics for the structurally free
logic LC+,” Logic Journal of IGPL,
9 (2001), pp. 525–539. (The paper
at OUP.)
