Research

Research Interests   Publications   Presentations   Other Activities   CV

 

Research Interests

 

Universal Algebra, Ordered Algebraic Structres and Algebraic Logic.
 

 

Publications

 

Book.

 

Residuated Lattices: an algebraic glimpse at substructural logics, with P. Jipsen, T. Kowalski and H. Ono, Studies in Logics and the Foundations of Mathematics, Elsevier, pp. 509+ (publication date, April 20, 2007).

 

 

Refereed papers.

 

1.      The undecidability of the word problem for distributive residuated lattices, Ordered Algebraic Structures (J. Martinez, ed.), Kluwer Academic Publishers, Dordrecht, 2002, 231-243.  (pdf)

 

2.      Cancellative residuated lattices,  with P. Bahls, J. Cole, P. Jipsen and C. Tsinakis, Algebra Universalis 50 (2003), no. 1, 83-106. (pdf)

 

3.      Equational bases for joins of residuated-lattice varieties, Studia Logica 76(2) (2004), 227-240. (pdf)

 

4.      Adding involution to residuated structures, with J. Raftery, Studia Logica 77(2) (2004), 181-207. (pdf)

 

5.      Generalized MV-algebras, with C. Tsinakis, Journal of Algebra 283(1) (2005), 254-291. (pdf)

 

6.      Minimal varieties of residuated lattices, Algebra Universalis 52(2) (2005), 215-239. (pdf)

 

7.      Algebraization, paremetrized local deduction theorem and interpolation for substructural logics over FL, with H. Ono, Studia Logica 83 (2006), 279-308. (pdf)

 

8.      Glivenko theorems for substructural logics over FL, with H. Ono, Journal of Symbolic Logic 71(4) (2006), 1353-1384. (pdf)

 

 

Work in progress.

 

Cut elimination and strong separation for substructural logics: an algebraic approach, with H. Ono, in preparation.

Equivalence of closure operators: an order-theoretic and categorical perspective, with C. Tsinakis, in preparation.

Residuated frames with applications to decidability, with P. Jipsen, in preparation.

The expressive power of structural rules for FL, with A. Ciabattoni and K. Terui, in preparation.

A Priestley duality for bounded distributive residuated lattices, in preparation.

The monoid reducts of residuated lattices, with S. Seif, in preparation.

 

Non-refereed conference proceedings.

 

Involutive commutative distributive residuated lattices, proceedings of the 37th Mathematical Logic Group Meeting, Shizuoka, 2003.

Extensions of Glivenko's theorem to non-commutative substructural logics, proceedings of the 39th Mathematical Logic Group Meeting, Gamagori, 2005.

 

Theses.

 

Varieties of residuated lattices, Ph. D. thesis, Department of Mathematics, Vanderbilt Universisty, 2003. (pdf)

Selected topics on residuated lattices, Qualifying paper, Department of Mathematics, Vanderbilt University, 2000. (pdf)


Educational publication.

From here to infinity: a foundation for Calculus, with J. Staples et al., Tomson Learning Custom Publishing, 2001.

 

Conference Presentations and Seminar Talks

 

 

Involutive FL-algebras and decidability, Invited Plenary talk, International conference on Order, Algebra and Logics, Vanderbilt University, USA, scheduled for June 2007.

Algebraic cut elimination, Seminar talk at the Logic Summer School, Australian National University, Canberra, Australia, December 2006.

Residuated frames, Workshop on Algebra and Substructural Logics III, Krakow, Poland, November 2006.

Cut elimination for substructural logics from a semantical perspective, Colloquium talk, Vienna University of Technology, November 2006.

Semantics for substructural logics, Colloquium talk, University of Milan, Italy, October 2006.

Decidability for involutive residuated lattices, Colloquium talk, Univesity of Szeged, Hungary, October 2006.

Glivenko theorems for substructural logics, Logic Colloquium 2006, Association for Symbolic Logic European Summer Meeting, Nijmegen, Netherlands, scheduled for July 2006.

Lack of structural rules and algebraic semantics, Ordered structures in many-valued logics, Massa Lubrense, Sorrento, Italy, May 2006.

Algebraic methods in substructural logics, Logic Colloquium 2005, Association for Symbolic Logic European Summer Meeting, Athens, Greece, July 2005.

Equivalence of consequence relations: an order-theoretic and categorical perspective, Algebraic and topological methods in non-classical logics II, Barcelona, Spain, June 2005.

Non-associative residuated lattices, AMS sectional meeting, special session on Universal Algebra and Lattice Theory, Vanderbilt University, October 2004.

Translations in substructural logic, Logic Colloquium 2004, ASL European Summer Meeting, Torino, Italy, July 2004.

Non-associative substructural logics: algebraization, cut elimination and separation, Conference on Residuated Structures and Many-Valued Logics, Patras University, Greece, June 2004.

Residuated lattices – an introduction, Department of Mathematics, Aristotle University of Thessaloniki, Greece, May 2004.

Involutive commutative distributive residuated lattices, 37th Mathematical Logic Group Meeting, Shizuoka, Japan, December 2003.

The join of finitely many varieties of residuated lattices, Annual Meeting of the Association for Symbolic Logic, special session on Algebraic Logic and Universal Algebra, University of Illinois at Chicago, June 2003.

Decision problems for commutative distributive residuated lattices, Colloquium talk, University of Saskatoon, Canada, May 2003.

Generalized MV-algebras, Conference on Ordered Algebraic Structures, Vanderbilt University, March 2003.

A Priestley duality for bounded distributive residuated lattices, Annual meeting of the American Mathematical Society, special session on The Many Lives of Lattice Theory and the Theory of Ordered Sets, with Connections to Combinatorics, Baltimore, January 2003.

A categorical equivalence for integral GMV-algebras, Workshop on Algebra and Substructural Logics, Japan Advanced Institute of Science and Technology, November 2002.

Integral generalized MV-algebras, Algebra Seminar, Vanderbilt University, October 2002.

Some atomic varieties of residuated lattices, Algebra Seminar, Vanderbilt University, September 2002.

Continuum many idempotent minimal residuated-lattice varieties, International Conference on Modern Algebra in conjunction with the 17th annual Shanks Lectures, Vanderbilt University, May 2002.

Varieties of residuated lattices generated by positive universal classes, Conference on Ordered Algebraic Structures, Vanderbilt University, March 2002.

The undecidability of the word problem for the variety of distributive residuated lattices, Conference on Lattice-Ordered Groups and f-Rings, University of Florida, March 2001.

The subvariety lattice of residuated lattices, Workshop on Ordered Algebraic Structures, Vanderbilt University, March 2000.

 

Other Academic Activities

 

Member of the Editorial Board for the journal Soft Computing.

Referee for the journals Journal of Symbolic Logic, Algebra Universalis, Studia Logica, Lecture Notes in Computer Science, Journal of Logic and Computation, Fuzzy Sets and Systems, Czechoslovak Mathematical Journal and Soft Computing.

Master Thesis Examiner  for Ms. Ai-ni Hsieh, University of Natal, South Africa (degree awarded in 2005). 

 

Curriculum Vitae


Here is a copy of my CV.

Back to the main page.