Fall 2019
Phil 220: Symbolic Logic 2
Phil 367: Introduction to the Philosophy of Mathematics
Winter 2020
Phil 422/Phil 522: Topic: Gödel's Incompleteness Theorems
Phil 325: Risk, Choice and Rationality
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: 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 λcalculi. 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
computer science 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 the philosophy of computer science and informatics,
especially, those that concern questions related to theoretical computer
science — like algorithmics, programming language design, information
theory, complexity theory 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., calculi 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.
(More info on the project.) The (first)
Third Workshop, which took place on May
16–17, 2016, at the University of Alberta, was thematically connected to
the same SSHRC IG. (The poster for the
workshop.) We continue to collaborate on questions related to various
relational semantics for substructural logics as part of a SSHRC
IG.
A more precise characterization of classes of structures for various
nonclassical logics leads straightforwardly to topological
frames. I proved 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.
A more precise characterization of classes of structures for various
nonclassical logics leads straightforwardly to topological
frames. I proved 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 λcalculi 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 calculi —
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. Also, combinatory
logic in itself is an elegant and powerful formalism that can
represent computable functions — just as, for instance,
register 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 calculi 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 calculi for some of these relevance logics
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, which extends a sequent calculus for implicational
T by two rules that add exactly what the difference between these
logics is. I wrote a book on
proof theory with a focus on sequent calculi (including some tableaux and
resolution systems). I proved the
decidability of MELL (the
multiplicative–exponential fragment of linear logic). J. Michael
Dunn and I proved the decidability of several modal relevance logics.
Last year, I proved another group of modal logics (certain semilattice based
modal logics) decidable. Of course, not all (propositional)
logics are decidable, but some of them are — even if their decidability
is surprising (to a few).
I am certain that logic — together with its many connections
and offsprings — is an exciting and thriving field of
research.

Mailing address:
University of Alberta
Department of Philosophy
240 Assiniboia Hall
Edmonton, AB T6G 2E7, Canada
Email address:
Page updated on:
December 3rd, 2019
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
Alter
ego page

 K. Bimbó, “On the algebraization of relevance logics. (A
preamble to J. Michael Dunn's PhD dissertation),” in Logic
PhDs, v. 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, v. 418, Springer
Nature, Switzerland, 2019, pp. 127–146. (The volume
@Springer.)
 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.
 K. Bimbó, J. M. Dunn and N. Ferenz, “Two manuscripts, one by
Routley, one by Meyer: The origins of the RoutleyMeyer semantics for
relevance logics,” Australasian Journal of Logic 15 (2018),
pp. 171–209. (The paper @VictoriaU.)
 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.
 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, v. 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, @
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.
 K. Bimbó, “The decidability of the intensional
fragment of classical linear logic,” Theoretical
Computer Science 597 (2015), pp. 1–17.
 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.)
 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.
 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.
 K. Bimbó and J. M. Dunn, “On the decidability
of implicational ticket entailment,” Journal of Symbolic
Logic 78(1) (2013), pp. 214–236.
[JSL @ CUP.]
 K. Bimbó and J. M. Dunn, “New consecution
calculi for R^{t}_{→},” Notre Dame Journal of Formal Logic
53(4) (2012), pp. 491–509.
[NDJFL @ 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.
 K. Bimbó, “Schönfinkeltype operators for classical logic,”
Studia Logica 95 (2010), pp. 355–378.
 K. Bimbó and J. M. Dunn, “Symmetric generalized Galois logics,” Logica Universalis 3 (2009), pp. 125–152.
 K. Bimbó, J. M. Dunn and R. D. Maddux, “Relevance logics and
relation algebras,” Review
of Symbolic Logic 2 (2009), pp. 102–131.
[RSL
@ CUP.]
 K. Bimbó, “Combinatory
logic,” Stanford Encyclopedia of Philosophy.
[SEP @ Stanford University.]
 K. Bimbó, “Dual gaggle semantics for entailment,”
Notre Dame Journal of Formal
Logic 50 (2009), pp. 23–41.
[NDJFL @ 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 University of Chicago Press.]
 K. Bimbó, “Functorial duality for
ortholattices and De Morgan lattices,” Logica
Universalis 1 (2007), pp. 311–333.
 K. Bimbó, “LE^{t}_{→},
LR^{°}_{ˆ˜}, LK and cut free proofs,”
Journal of Philosophical Logic 36 (2007),
pp. 557–570.
 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.
 K. Bimbó, “The ChurchRosser property in symmetric
combinatory logic,” Journal of
Symbolic Logic 70 (2005), pp. 536–556. [JSL 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.
[NDJFL @ Project Euclid.]
 K. Bimbó, “Types of Ifree hereditary right
maximal terms,” Journal
of Philosophical Logic 34 (2005), pp. 607–620.
 K. Bimbó, “Semantics for dual and symmetric
combinatory calculi,” Journal
of Philosophical Logic, 33 (2004), pp. 125–153.
 K. Bimbó, “A set theoretical semantics for full propositional linear
logic,” (abstract), Bulletin
of Symbolic Logic 10 (2004), p. 136.
[BSL
@ CUP.]
 K. Bimbó, “The ChurchRosser property in dual combinatory
logic,” Journal of
Symbolic Logic 68 (2003), pp. 132–152. [JSL
@ JSTOR.]
 K. Bimbó and J. M. Dunn, “Fourvalued
logic,” Notre Dame Journal of
Formal Logic 42 (2002), pp. 171–192.
[NDJFL @ Project Euclid.]
 K. Bimbó, “Semantics for the structurally free
logic LC+,” Logic Journal of IGPL,
9 (2001), pp. 525–539.
