CURRICULUM VITAE: J G RAFTERY

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1 CURRICULUM VITAE: J G RAFTERY Name: James Gordon Raftery Address: School of Mathematical Sciences, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban, 4000 South Africa. Tel: (W); (H). Fax: / raftery@ukzn.ac.za Date of Birth: January 7, 1961 Academic Record B.A. (Hons.) (Math.) (with distinction), University of Natal, Pietermaritzburg, H.D.E. (Post-graduate), University of Natal, Durban, M.A. (Math.) (with distinction), University of Natal, Durban, Thesis: On strongly prime rings and modules. Supervisor: Professor A.R. Meijer. Ph.D. (Math.), University of Natal, Durban, Thesis: On ideals, congruences and extensions of BCK-algebras. Supervisor: Professor T. Sturm. Employment 2004 present: Professor, School of Mathematical Sciences, University of KwaZulu- Natal, Durban. [The Universities of Natal and Durban-Westville merged on January 1, 2004 to form the University of KwaZulu-Natal.] : Professor, School of Mathematical and Statistical Sciences, University of Natal, Durban : Associate Professor, School of Mathematical and Statistical Sciences [formerly Department of Mathematics and Applied Mathematics], University of Natal, Durban : Associate Professor, Department of Mathematics and Applied Mathematics, University of Natal, Pietermaritzburg : Senior Lecturer, same department : Lecturer, same department. 1

2 2 CURRICULUM VITAE: J G RAFTERY RESEARCH OUTPUTS Publications 1. Raftery J.G. On prime ideals and subdirect decompositions of BCK algebras, Mathematica Japonica 32 (5) (1987), Raftery J.G. On some special classes of prime rings, Quaestiones Mathematicae 10 (3) (1987), Raftery J.G. On some rings whose injective hulls have few preradical submodules, Quaestiones Mathematicae 10 (4) (1987), Raftery J.G. and Sturm T. On BCK algebras embeddable into bounded BCKalgebras, Mathematica Japonica 32 (1) (1987), Raftery J.G. and Sturm T. On ideal and congruence lattices of BCK semilattices, Mathematica Japonica 32 (3) (1987), Raftery J.G. and Sturm T. On an embedding of distributive nearlattice BCK algebras into distributive lattice BCK algebras, Mathematica Japonica 33 (2) (1988), Raftery J.G. and Sturm T. On completions of pseudo-normed BCK-algebras and pseudo-metric universal algebras, Mathematica Japonica 33 (6) (1988), Meijer A.R. and Raftery J.G. A note on comparative purities relative to torsion preradicals, Anales del Instituto de Matematicas. Universidad Nacional Autonoma de Mexico 30 (1990), Raftery J.G. and Sturm T. Completions of uniform universal algebras and strongly uniform BCK algebras, Demonstratio Mathematica 23 (2) (1990), Raftery J.G., Rosenberg I.G. and Sturm T. Tolerance relations and BCK algebras, Mathematica Japonica 36 (3) (1991), Raftery J.G. and Sturm T. On direct products of BCK chains, Mathematica Japonica 36 (1) (1991), Raftery J.G. and Sturm T. On the semiprime ideal lattice of a right invariant ring, Quaestiones Mathematicae 14 (3) (1991), Raftery J.G. and Sturm T. Tolerance numbers, congruence n permutability and BCK algebras, Czechoslovak Mathematical Journal 42 (117) (1992), Raftery J.G. and van den Berg J.E. On a classification of prime rings, Quaestiones Mathematicae 15 (2) (1992), Blok W.J. and Raftery J.G. Failure of the congruence extension property in BCK algebras and related structures, Mathematica Japonica 38 (4) (1993), Van den Berg J.E. and Raftery J.G. Every algebraic chain is the congruence lattice of a ring, Journal of Algebra 162 (1) (1993), Raftery J.G. Ideal determined varieties need not be congruence 3 permutable, Algebra Universalis 31 (2) (1994),

3 CURRICULUM VITAE: J G RAFTERY Van den Berg J.E. and Raftery J.G. On rings (and chains domains) with restricted completeness conditions on topologizing filters, Communications in Algebra 22 (4) (1994), Blok W.J. and Raftery J.G. On the quasivariety of BCK algebras and its subvarieties, Algebra Universalis 33 (1) (1995), Raftery J.G. and van den Berg J.E. On prime rings and the radicals associated with their degrees of primeness, Quaestiones Mathematicae 18 (4) (1995), Raftery J.G. and Sturm T. On hereditary subalgebras of BCK algebras, Demonstratio Mathematica 29 (1) (1996), Barbour G.D. and Raftery J.G. On the degrees of permutability of subregular varieties, Czechoslovak Mathematical Journal 47(122) (1997), Barbour G.D. and Raftery J.G. Ideal determined varieties have unbounded degrees of permutability, Quaestiones Mathematicae 20 (4) (1997), Blok W.J. and Raftery J.G. Varieties of commutative residuated integral pomonoids and their residuation subreducts, Journal of Algebra 190 (2) (1997), Raftery J.G. and van Alten C.J. On the algebra of noncommutative residuation: Polrims and left residuation algebras, Mathematica Japonica 46 (1) (1997), Van Alten C.J. and Raftery J.G. On quasivariety semantics of fragments of intuitionistic propositional logic without exchange and contraction rules, Reports on Mathematical Logic 31 (1997), Blok W.J. and Raftery J.G. Ideals in quasivarieties of algebras, Models, Algebras and Proofs (X. Caicedo and C.H. Montenegro, eds.), Lecture Notes in Pure and Applied Mathematics, Vol. 203, Marcel Dekker, New York, 1999, pp Van Alten C.J. and Raftery J.G. The finite model property for the implicational fragment of IPC without exchange and contraction, Studia Logica 63 (2) (1999), Van Alten C.J. and Raftery J.G. On the lattice of varieties of residuation algebras, Algebra Universalis 41 (4) (1999), Raftery J.G. and van Alten C.J. Residuation in commutative ordered monoids with minimal zero; and Corrigendum, Reports on Mathematical Logic 34 (2000), 23 57; and 39 (2005), Blok W.J. and Raftery J.G. On congruence modularity in varieties of logic, Algebra Universalis 45 (1) (2001), Raftery J.G. A characterization of varieties, Algebra Universalis 45 (4) (2001), Barbour G.D. and Raftery J.G. Quasivarieties of logic, regularity conditions and parameterized algebraization, Studia Logica 74 (1 2) (2003), Blok W.J. and Raftery J.G. Constructing simple residuated lattices, Algebra Universalis 50 (3 4) (2003), Blok W.J. and Raftery J.G. Fragments of R mingle, Studia Logica 78 (1 2) (2004),

4 4 CURRICULUM VITAE: J G RAFTERY 36. Galatos N. and Raftery J.G. Adding involution to residuated structures, Studia Logica 77 (2) (2004), Raftery J.G. Willem Blok s work in algebraic logic, Studia Logica 76 (2) (2004), Van Alten C.J. and Raftery J.G. Rule separation and embedding theorems for logics without weakening, Studia Logica 76 (2) (2004), Hsieh A. and Raftery J.G. A finite model property for RMI min, Mathematical Logic Quarterly 52 (6) (2006), Raftery J.G. Correspondences between Gentzen and Hilbert systems, The Journal of Symbolic Logic 71 (3) (2006), Raftery J.G. The equational definability of truth predicates, Reports on Mathematical Logic (Special Issue in Memory of W.J. Blok) 41 (2006), Hsieh A. and Raftery J.G. Conserving involution in residuated structures, Mathematical Logic Quarterly 53 (6) (2007), Olson J.S. and Raftery J.G. Positive Sugihara monoids, Algebra Universalis 57 (1) (2007), Raftery J.G. Representable idempotent commutative residuated lattices, Transactions of the American Mathematical Society 359 (9) (2007), Raftery J.G. On the variety generated by involutive pocrims, Reports on Mathematical Logic 42 (2007), Blok W.J. and Raftery J.G. Assertionally equivalent quasivarieties, International Journal of Algebra and Computation 18 (4) (2008), Galatos N., Olson J.S. and Raftery J.G. Irreducible residuated semilattices and finitely based varieties, Reports on Mathematical Logic 43 (2008), Olson J.S. and Raftery J.G. Residuated structures, concentric sums and finiteness conditions, Communications in Algebra 36 (10) (2008), Olson J.S., Raftery J.G. and van Alten C.J. Structural completeness in substructural logics, Logic Journal of the IGPL 16 (5) (2008), Hsieh A. and Raftery J.G. Semiconic idempotent residuated structures, Algebra Universalis 61 (3 4) (2009), Raftery J.G. A non-finitary sentential logic that is elementarily algebraizable, Journal of Logic and Computation 20 (4) (2010), Papers Accepted for Publication 52. Raftery J.G. A perspective on the algebra of logic, Quaestiones Mathematicae, to appear. Papers Submitted for Publication 53. Raftery J.G. Order algebraizable logics. 54. Raftery J.G. Admissible rules and the Leibniz hierarchy. Papers in Preparation 55. Raftery J.G. Contextual deduction theorems.

5 Other Research Outputs CURRICULUM VITAE: J G RAFTERY 5 Raftery J.G. and van Alten C.J. On the algebra of noncommutative residuation; exchange-free intuitionistic propositional logic. Abstract. Workshop on Abstract Algebraic Logic, July 1 5, 1997, Centre de Recerca Matemàtica, Bellaterra (Spain). 11pp. Supervision of Graduate Students PhD Students 1. J.E. van den Berg, PhD, completed Thesis title: On chain domains, prime rings and torsion preradicals. 2. C.J. van Alten, PhD, completed Thesis title: An algebraic study of residuated ordered monoids and logics without exchange and contraction. 3. J.S. Olson, PhD, completed Thesis title: Finiteness conditions on varieties of residuated structures. 4. A. Hsieh, PhD, completed Thesis Title: Embedding theorems and finiteness properties for residuated structures and substructural logics. MSc Students 5. C.J. van Alten, MSc, completed with distinction Thesis title: Algebraizing deductive systems. 6. G.D. Barbour, MSc, completed with distinction, Thesis title: On regularity, ideal determination and related Mal cev properties of varieties of algebras. 7. I. Swart, MSc, completed with distinction, Thesis title: Residually small varieties and commutator theory. 8. A. Hsieh, MSc, completed with distinction, Thesis title: Logics with the mingle and contraction axioms. Editorship: Member of Editorial Board of Algebra Universalis, since Joint editor (with J. Berman, W. Dziobiak and D. Pigozzi) of the special issue of Studia Logica in memory of W.J. Blok, Vol. 83 Nos. 1 3, Refereeing: I have refereed for the following journals: Algebra Universalis Applied Categorical Stuctures Bulletin of the Iranian Mathematical Society Demonstratio Mathematica Fuzzy Sets and Systems Houston Journal of Mathematics

6 6 CURRICULUM VITAE: J G RAFTERY Indian Journal of Pure and Applied Mathematics International Journal of Mathematics and Mathematical Sciences The Journal of Algebra The Journal of Logic and Computation The Journal of Symbolic Logic Logic Journal of the IGPL Mathematica Japonica Mathematical Logic Quarterly Multiple Valued Logic Order Proceedings of the American Mathematical Society Quaestiones Mathematicae Reports on Mathematical Logic Studia Logica Vietnam Journal of Mathematics Talks Given 1. On boundedness in strongly semiprime rings, Paper given at the Annual Congress of the South African Mathematics Society. Pretoria, Embedding certain BCK-algebras into distributive lattice BCK-algebras, Paper given at Interdisciplinary Conference on Mathematical Logic and related subjects. Durban, Some structure theorems for BCK-algebras, Paper given at the Annual Congress of the South African Mathematics Society. Stellenbosch, Ideal and congruence lattices of BCK-semilattices, Paper given at International Conference on Universal Algebra, Lattices and Semigroups. Lisbon, Portugal, Representation theorems for some lattices associated with rings, Paper given at the Annual Congress of the South African Mathematics Society. Berg-en-Dal, On some special classes of prime rings, Paper given at the First Kwazulu-Natal Mathematics Conference. Umlazi, Tolerance relations on algebraic structures, Paper given at the Second Kwazulu- Natal Mathematics Conference. Durban, Tolerance numbers and congruence n-permutability of algebras, Annual Congress of the South African Mathematics Society. Mmabatho, On algebraic structures with compatible uniformities, Paper given at the Third Kwazulu-Natal Mathematics Conference. Pietermaritzburg, On rings whose torsion preradicals commute with certain direct products, Paper given at the ICOR 91 Conference on the Theory of Radicals. Szekszárd, Hungary, 1991.

7 CURRICULUM VITAE: J G RAFTERY Rings with restricted completeness conditions on topologizing filters, Paper given at the Warwick Algebra Symposium. Coventry, England, Ideals in universal algebra, Paper given at the Fourth Kwazulu-Natal Mathematics Conference. Durban-Westville, Every algebraic chain is the congruence lattice of a ring, Paper given at the Alan Day Conference on Lattices and Algebras. Hamilton, Ontario, Canada, The High School Identities, Paper given at the Fifth Kwazulu-Natal Mathematics Conference. Kwa-Dlangezwa, Ideals in varieties of algebras, Paper given at the Annual Congress of the South African Mathematical Society. Pietermaritzburg, On implies and minus and plus and topologizing filters on rings, Paper given at the Sixth Kwazulu-Natal Mathematics Conference. Durban, Ultraproducts: what and why?, Paper given at the Seventh Kwazulu-Natal Mathematics Conference. Durban, Residuated commutative ordered monoids in algebra and logic. The ordinal sum construction, Paper given at the Annual Congress of the South African Mathematical Society. Durban-Westville, Abstracting commutativity, Paper given at the Eighth Kwazulu-Natal Mathematics Conference. Pietermaritzburg, Ordinal sum construction in varieties of residuated pomonoids, Paper given at the International Conference on Modern Algebra and its Applications. Nashville, Tennessee, USA, Ideal theory for quasivarieties of algebras, Paper given at the Annual Congress of the South African Mathematical Society. Bellville, On lattices of varieties of residuation (and BCK) algebras, Paper given at the Joint Annual Congress of the South African and American Mathematical Societies. Pretoria, On the algebra of noncommutative residuation: exchange-free intuitionistic propositional logic, Invited paper given at the Workshop on Abstract Algebraic Logic. Barcelona, Spain, On a classification of all finite algebras, Paper given at the Tenth Kwazulu- Natal Mathematics Conference. Umlazi, On the equational definability of principal congruence meets for certain algebras, Paper given at the Annual Congress of the South African Mathematical Society. Johannesburg, Assertionally conservative and semiregular quasivarieties, Paper given at the Holiday Symposium on Algebraic Logic, New Mexico State University. Las Cruces, New Mexico, USA, Residual size does matter, Paper given at the Eleventh Kwazulu-Natal Mathematics Conference. Durban, Varieties of logic and congruence modularity, Paper given at the Annual Congress of the South African Mathematical Society. Pietersburg, 1999.

8 8 CURRICULUM VITAE: J G RAFTERY 29. Residuation in commutative pomonoids with minimal unit. An algebraizable extension of BCI, Invited paper given at the Workshop on Algebra and Substructural Logics. Tatsunokuchi, Ishikawa, Japan, On assertional logic. Paper given at the Mini-Conference on Algebraic Logic, University of Illinois at Chicago, USA, Fragments of relevance logic with the mingle axiom, Paper given at the Annual Congress of the South African Mathematical Society. Durban-Westville, Some neglected questions about R-mingle, Paper given at the Fourteenth Kwazulu-Natal Mathematics Conference. Durban, On assertional equivalence of quasivarieties, Invited paper given at the Special Session on Universal Algebra and Algebraic Logic, Joint Annual Congress of the Italian and American Mathematical Societies, Pisa, Consequence fragments of R-mingle, Invited paper given at the second Workshop on Algebra and Substructural Logics. Tatsunokuchi, Ishikawa, Japan, Adding negation, Paper given at the Fifteenth Kwazulu-Natal Mathematics Conference. Durban-Westville, Axiomatics and the Twentieth Century, Inaugural Lecture, University of Natal, Durban, June 25, Willem Blok s work in algebraic logic, Invited colloquium lecture, University of Illinois at Chicago, USA, Adding involution to residuated structures, Paper given at the International Conference on Residuated Structures, Patras, Greece, Structural completeness in substructural logics, Plenary talk given at International Conference on Algebraic and Topological Methods in Non-Classical Logics, Barcelona, The equational definability of truth predicates, Invited colloquium lecture, New Mexico State University, Las Cruces, May Residuated structures, concentric sums and finiteness conditions, Invited paper given at the third Workshop on Algebra and Substructural Logics, Krakow, Poland, The equational definability of truth predicates, Selected plenary talk given at the First International Conference on Order, Algebra and Logics, Nashville, USA, June Doubts about N, Paper given at the Twentieth KwaZulu-Natal Mathematics Conference, Westville, Durban, Algebra of Logic, Two invited tutorials delivered at the BLAST 08 Conference, Denver University, Denver, USA, August Some recent developments in the algebra of logic, Paper given at the 51st Annual Congress of the South African Mathematical Society, Durban, November Order algebraizable logics, Selected plenary paper given at the TACL 09 Conference, Amsterdam, July 2009.

9 CURRICULUM VITAE: J G RAFTERY Finiteness properties for idempotent residuated structures, Paper given at the fourth Workshop on Algebra and Substructural Logics, Tatsunokuchi, Ishikawa, Japan, June Deductive systems: equivalence, algebraization and the Leibniz hierarchy, Invited paper given at the conference Diversity in Mathematics, African Institute of Mathematical Sciences, Muizenberg, Cape Town, July Admissible rules and the Leibniz hierarchy, Invited plenary paper given at the international conference Logic, Algebra and Truth Degrees 2010, Prague, September Idempotent residuated structures and finiteness conditions, Invited paper given at the Workshop on Logic and Algebra, Stellenbosch, 2 October J.G. RAFTERY (6 February 2011)

Logics preserving degrees of truth and the hierarchies of abstract algebraic logic

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