Bimbo, Katalin - Department of Philosophy

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Bimbo, Katalin

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Appointment effective July 1, 2008.

Katalin Bimbó
Assistant professor

Academic qualifications

   1986: Dipl. (philosophy), Moscow State University
   1994: Doctorate (logic), Eötvös University
   1999: PhD (philosophy and cognitive science), Indiana University Bloomington

Research

My main research area is logic. I am especially interested in nonclassical logics, including relevance and substructural logics, combinatory logics and λ-calculi. Nonclassical logics were originally introduced as a solution to philosophical problems such as the problem of implication and entailment. Further new logics emerged in many disciplines from mathematics and computer science to linguistics. Some of my research interests—beyond logic and the philosophy of logic—are connected to those areas. I maintain an active interest in the philosophy of computer science and informatics, especially, in questions related to theoretical computer science (such as algorithmics, programming language design, information theory, complexity theory and cyber security). I have worked on the semantics of natural languages (primarily, using modal logics and discourse representation theory), and I am interested in the philosophy of mathematics, in particular, in the foundations of mathematics.

Some of my research results concern semantics for various nonclassical logics (e.g., combinatory systems). J. Michael Dunn and I wrote a book on the relational semantics of nonclassical logical calculi. These kinds of semantics generalize Kripke’s possible worlds semantics for normal modal logics, and have been the preferred sort of semantics for decades. Earlier, we worked out representations for the Kleene logic and action logic (which are closely related to dynamic logic). We also collaborated on defining a four-valued semantics for the minimal substructural logic.

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, because the (algebras of) logics are treated abstractly as categories (in the sense of category theory), where the morphisms of the category are interpretations of the logic.

The proof theory of nonclassical logics sometimes gets tricky. The classical sequent calculus (LK) is a seemingly simple proof system, but in reality, the proofs are tightly controlled—as evidenced by the cut theorem. Some well-known relevance logics cannot be formalized as extensions of the associative Lambek calculus and this effects various “technical complications.” I succeeded in defining sequent calculi for some of these relevance logics together with proving the cut theorem for them. The purely inductive proofs that I used to show the cut theorem for the single cut rule yield a purely inductive proof for the original classical sequent calculus (without a detour through mix).

Combinatory logics and λ-calculi are tied to other nonclassical logics in various ways, one of which is the Curry–Howard correspondence. The view that combinatory terms encode proofs leads to new notions in the proof theory of nonclassical logics and to new questions in combinatory logic. I am currently working on a major project in this area that continues some of my earlier research.

I believe (obviously) that logic together with its many connections and offsprings is a prosperous and exciting research area.

Teaching

In the fall term of the 2009/10 academic year I teach the following courses: Phil 522/420: Topics in logic/Metalogic, Phil 220: Symbolic logic 2 and Phil 325: Risk, choice and rationality.

In the winter term of the 2009/10 academic year I will teach a Phil 120: Symbolic logic 1 course.

Selected publications

K. Bimbó and J. M. Dunn, “Calculi for symmetric generalized Galois logics,” in J. van Benthem, M. Moortgat and W. Buszkowski (eds.), A Festschrift for Joachim (Jim) Lambek, (v. 36 of Linguistic Analysis), (37 pages), to appear.
(Linguistic Analysis online.)
K. Bimbó and J. M. Dunn, “Symmetric generalized Galois logics,” Logica Universalis 3 (2009), pp. 125–152.
(Logica Universalis at Springer.)
K. Bimbó, J. M. Dunn and R. D. Maddux, “Relevance logics and relation algebras,” Review of Symbolic Logic 2 (2009), pp. 102–131.
(Review of Symbolic Logic at Cambridge University Press.)
K. Bimbó, “Combinatory logic,” Stanford Encyclopedia of Philosophy.
(SEP at Stanford University.)
K. Bimbó, “Dual gaggle semantics for entailment,” Notre Dame Journal of Formal Logic 50 (2009), pp. 23–41.
(Notre Dame Journal of Formal Logic at 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.
(CSLI Publications's web site and the University of Chicago Press's web site.)
K. Bimbó, “Functorial duality for ortholattices and De Morgan lattices,” Logica Universalis, 1 (2007), pp. 311–333.
(Logica Universalis at Springer.)
K. Bimbó, “LE^t_→, LR^°_{_ˆ˜}, LK and cut free proofs,” Journal of Philosophical Logic, 36 (2007), pp. 557–570.
(Journal of Philosophical Logic at Springer.)
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 (North-Holland), 2006, pp. 723–789,
(Handbook of the Philosophy of Science project and the volume's description at Elsevier.)
K. Bimbó, “Admissibility of cut in LC with fixed point combinator,” Studia Logica 81 (2005), pp. 399–423.
(Studia Logica at Springer.)
K. Bimbó, “The Church-Rosser property in symmetric combinatory logic,” Journal of Symbolic Logic 70 (2005), pp. 536–556.
(Journal of Symbolic Logic at Project Euclid.)
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.
(Notre Dame Journal of Formal Logic at Project Euclid.)
K. Bimbó, “Types of I-free hereditary right maximal terms,” Journal of Philosophical Logic 34 (2005), pp. 607–620.
(Journal of Philosophical Logic at Springer.)
K. Bimbó, “Semantics for dual and symmetric combinatory calculi,” Journal of Philosophical Logic, 33 (2004), pp. 125–153.
(Journal of Philosophical Logic at Springer.)
K. Bimbó, “A set theoretical semantics for full propositional linear logic,” (abstract), Bulletin of Symbolic Logic 10 (2004), pp. 136.
K. Bimbó, “The Church-Rosser property in dual combinatory logic,” Journal of Symbolic Logic 68 (2003), pp. 132–152.
(Journal of Symbolic Logic at Project Euclid.)
K. Bimbó and J. M. Dunn, “Four-valued logic,” Notre Dame Journal of Formal Logic 42 (2002), pp. 171–192.
(Notre Dame Journal of Formal Logic at Project Euclid.)
K. Bimbó, “Semantics for the structurally free logic LC+,” Logic Journal of IGPL, 9 (2001), pp. 525–539. (Journal of IGPL at Oxford University Press)
K. Bimbó, “Kripke semantics for structurally free logics without distributivity,” (abstract), Bulletin of Symbolic Logic, 6 (2000), pp. 248–249.
K. Bimbó and J. M. Dunn, “Two extensions of the structurally free logic LC,” Logic Journal of IGPL 6 (1998), pp. 403–424.
(Journal of IGPL at Oxford University Press)
K. Bimbó, “Specificity and definiteness of temporality in Hungarian,” In: J. Bernard and K. Neumer (eds.), Zeichen, Sprache, Bewuβtsein. Österreichisch–Ungarische Dokumente zur Semiotik und Philosophie 2, ÖGS–ISSS, Wien–Budapest, 1994, pp. 7–25.
K. Bimbó, “Are the ‘and’ and ‘.’ the same sentence connectives?,” In: J. Darski and Z. Vetulani (eds.), Akten des 26. linguistischen Kolloquiums, v.2, Max Niemeyer, Tübingen, 1993, pp. 485–490.
K. Bimbó and A. Mátè, (eds.) Proceedings of the 4th Symposium on Logic and Language, Áron Publishers, Budapest, 1993.
K. Bimbó, “On the problem of conditional statements,” In: V. A. Smirnov, P. I. Bystrov and A. S. Karpenko (eds.), Filosofskie osnovaniya neklassicheskikh logik, Institut Filosofii AN SSSR, Moscow, 1990, pp. 12–25.
K. Bimbó, “Translation of three-valued logics into sequent calculi,” In: Yu. V. Ivlev (ed.), Sovremennaya logika i metodologiya nauki, Izdatel’stvo MGU, Moscow, 1987, pp. 108–119.