A mathematical life. (English) Zbl 1396.03003
Czelakowski, Janusz (ed.), Don Pigozzi on abstract algebraic logic, universal algebra, and computer science. Cham: Springer (ISBN 978-3-319-74771-2/hbk; 978-3-319-74772-9/ebook). Outstanding Contributions to Logic 16, 1-51 (2018).
Summary: Here is the story of my forty years as a professional algebraist and logician and also as a computer science dilettante. It is divided into seven parts chronologically. Each part begins with a narrative in which I describe my relationship with mentors, colleagues, collaborators, and students, often in very personal terms.
For the entire collection see [Zbl 1390.03005].
For the entire collection see [Zbl 1390.03005].
MSC:
| 03-03 | History of mathematical logic and foundations |
| 01A70 | Biographies, obituaries, personalia, bibliographies |
Biographic References:
Pigozzi, DonReferences:
| [1] | Adams, M. and Pigozzi, D. and Sichler, J. (1981). Endomorphisms of direct unions of bounded lattices, \(Archiv der Mathematik\)36(1), 221-229. · Zbl 0443.06007 |
| [2] | Bergman, C. H. and Maddux, R. D. and Pigozzi D. (1990). \(Algebraic logic and universal algebra in computer science\), Volume 425. Lecture Notes in Computer Science, Conference, Ames Iowa, USA, June 1988. · Zbl 0779.00012 |
| [3] | Blok, W. J. and Köhler, P. and Pigozzi, D. (1984). On the structure of varieties with equationally definable principal congruences, II, \(Algebra Universalis\)18, 334-379. · Zbl 0558.08001 |
| [4] | Blok, W. J. and Pigozzi, D. (1982). On the structure of varieties with equationally definable principal congruences, I, \(Algebra Universalis\)13, 195-227. · Zbl 0512.08002 |
| [5] | Blok, W. J. and Pigozzi, D. (1986a). A finite basis theorem for quasivarieties, \(Algebra Universalis\)22(1), 1-13. · Zbl 0569.08004 |
| [6] | Blok, W. J. and Pigozzi, D. (1986b). Protoalgebraic logics, 45, 337-369. · Zbl 0622.03020 |
| [7] | Blok, W. J. and Pigozzi, D. (1988). Alfred Tarski’s work on general metamathematics, \(The Journal of Symbolic Logic\)53 (01), 36-50. · Zbl 0651.03002 |
| [8] | Blok, W. J. and Pigozzi, D. (1989, January). \(Algebraizable logics\), Volume 396, \(Memoires of the American Mathematical Society\), Providence. · Zbl 0664.03042 |
| [9] | Blok, W. J. and Pigozzi, D. (1991). \(Algebraic Logic\), Volume 50 of Studia Logica, Invited papers. · Zbl 0755.03034 |
| [10] | Blok, W. J. and Pigozzi, D. (1991b). Local deduction theorems in algebraic logic, In J. D. Andréka, H. Monk and I. Németi (Eds.), \(Algebraic Logic (Proc. Conf. Budapest 1988)\), Volume 54 of \(Colloq. Math. Soc. János Bolyai\), pp. 75-109. Amsterdam: North-Holland. · Zbl 0751.03036 |
| [11] | Blok, W. J. and Pigozzi, D. (1992). Algebraic semantics for universal Horn logic without equality, In A. Romanowska and J. D. H. Smith (Eds.), \(Universal Algebra and Quasigroup Theory\), Volume 19 of \(Research and Exposition in Mathematics\), pp. 1-56. Berlin: Heldermann Verlag. · Zbl 0768.03008 |
| [12] | Blok, W. J. and Pigozzi, D. (1994a). On the structure of varieties with equationally definable principal congruences, III, \(Algebra Universalis\)32, 545-608. · Zbl 0817.08004 |
| [13] | Blok, W. J. and Pigozzi, D. (1994b). On the structure of varieties with equationally definable principal congruences, IV, \(Algebra Universalis\)31, 1-35. · Zbl 0817.08005 |
| [14] | Blok, W. J. and Pigozzi, D. (1997). On the congruence extension property, \(Algebra Universalis\)38(4), 391-394. · Zbl 0934.08003 |
| [15] | Blok, W. J. and Pigozzi, D. (2003). Abstract algebraic logic and the deduction theorem, Manuscript. |
| [16] | Bowers, S. E. and Lewin, R. A. and Pigozzi, D. (2001). An annotated logic defined by a matrix, In J. Abe and S. Tanaka (Eds.), \(Unsolved Problems on Mathematic for the 21th Century-A Trubute to Kioshe Iseki’s 80th Birthday\). Amsterdam: IOS Press. · Zbl 0972.00067 |
| [17] | Czelakowski, J. and Pigozzi, D. (1999). Amalgamation and interpolation in abstract algebraic logic, In X. Caicedo and C. M. Montenegro (Eds.), \(Models, Algebras, and Proofs\), Volume 203 of \(Lecture Notes in Pure and Applied Mathematics\), pp. 187-265. New York, Basel: Marcel Dekker, Inc., Selected papers of the X Latin American symposium on mathematical logic held in Bogotá. · Zbl 0927.03086 |
| [18] | Czelakowski, J. and Pigozzi, D. (2004a). Fregean logics, \(Annals of Pure and Applied Logic\)127, 17-76, Provinces of logic determined. Essays in the memory of Alfred Tarski. Parts IV, V and VI. Eds: Z. Adamowicz, S. Artemov, D. Niwiński, E. Orƚowska, A. Romanowska and J. Woleński. · Zbl 1076.03045 |
| [19] | Czelakowski, J. and Pigozzi, D. (2004b). Fregean logics with the multiterm deduction theorem and their algebraization, \(Studia Logica\)78, 171-212. · Zbl 1058.03078 |
| [20] | Font, J. M. and Jansana, R. and Pigozzi, D. (2000a). \(Abstract algebraic logic I\), Volume 65. Studia Logica, ProceedingsWorkshop on Abstract Algebraic Logic, Centre de Recerca Matemàtica, Bellaterra (Spain), 1-5 July 1997. · Zbl 0953.00030 |
| [21] | Font, J. M. and Jansana, R. and Pigozzi, D. (2000b). Foreward to “Abstract algebraic logic I”, \(Studia Logica\)65(1), 1-9, Special issue devoted to the first volume of the Proceedings of the Workshop on Abstract Algebraic Logic. Editors J. M. Font, R. Jansana, and D. Pigozzi. Centre de Recerca Matemàtica, Bellaterra (Spain), 1-5 July 1997. · Zbl 0953.00030 |
| [22] | Font, J. M. and Jansana, R. and Pigozzi, D. (2001). Fully adequate Gentzen systems and the deduction theorem, \(Reports on Mathematical Logic\), Volume 35:115-165. · Zbl 1004.03053 |
| [23] | Font, J. M. and Jansana, R. and Pigozzi, D. (2003a). \(Abstract algebraic logic II\), Volume 74. Studia Logica, Proceedings Workshop on Abstract Algebraic Logic, Centre de Recerca Matemàtica, Bellaterra (Spain), 1-5 July 1997. |
| [24] | Font, J. M. and Jansana, R. and Pigozzi, D. (2003b). Foreward to “Abstract algebraic logic II”, \(Studia Logica\)74(1-2), 1-9, Special issue devoted to the second volume of the Proceedings of the Workshop on Abstract Algebraic Logic. Editors J. M. Font, R. Jansana, and D. Pigozzi. Centre de Recerca Matemàtica, Bellaterra (Spain), 1-5 July 1997. |
| [25] | Font, J. M. and Jansana, R. and Pigozzi, D. (2003c). A survey of abstract algebraic logic, \(Studia Logica\)74(1-2), 13-97. · Zbl 1057.03058 |
| [26] | Font, J. M. and Jansana, R. and Pigozzi, D. (2006). Fully adequate Gentzen systems and closure properties of the class of full models, In D. P. J. Berman, W. Dziobiak and J. Raftery (Eds.), \(Studia Logica. Special issue in memory of Willem Johannes Blok\), Volume 83. Springer. · Zbl 1106.03060 |
| [27] | Font, J. M. and Jansana, R. and Pigozzi, D. (2009). Update to “A survey of abstract algebraic logic”, \(Studia Logica\)91(1), 125-130. · Zbl 1162.03322 |
| [28] | Köhler, P. and Pigozzi, D. (1980). Varieties with equationally definable principal congruences, \(Algebra Universalis\)11(1), 213-219. · Zbl 0448.08005 |
| [29] | Leavens, G. and Pigozzi, D. (2002). Equational reasoning with subtypes, Technical Report #02-07, Iowa State University Department of Computer Science. |
| [30] | Leavens, G. T. and Pigozzi, D. (1991). Typed homomorphic relations extended with subtypes, In A. M. S. Brooks, M. Main and D. Schmidt (Eds.), \(International Conference on Mathematical Foundations of Programming Semantics\), Volume 598 of \(Lecture Notes in Computer Science\), pp. 144-167. · Zbl 1518.68056 |
| [31] | Leavens, G. T. and Pigozzi, D. (1997). The behavior-realization adjunction and generalized homomorphic relations, \(Theoretical Computer Science\)177(1), 183-216. · Zbl 0901.68123 |
| [32] | Leavens, G. T. and Pigozzi, D. (1998). Class-based and algebraic models of objects, \(Electronic Notes in Theoretical Computer Science\)14, 214-244. |
| [33] | Leavens, G. T. and Pigozzi, D. (2000). A complete algebraic characterization of behavioral subtyping, \(Acta Informatica\)36(8), 617-633. · Zbl 0951.68018 |
| [34] | Martins, M. A. and Pigozzi, D. (2007). Behavioural reasoning for conditional equations, \(Mathematical Structures in Computer Science\)17(05), 1075-1113. · Zbl 1129.68025 |
| [35] | Mobasher, B. and Leszczylowski, J. and Slutzki, G. and Pigozzi, D. (1993a, May), A knowledge-based procedural semantics for logic programming, Technical Report #93-15, Iowa State University, Department of Computer Science. |
| [36] | Mobasher, B. and Leszczylowski, J. and Slutzki, G. and Pigozzi, D. (1993b). Negation as partial failure, In I. M. Pereira and A. Nerode (Eds.), \(Logic programming and non-monotonic reasoning. Proceedings 2nd international workshop\), pp. 244-262. · Zbl 0850.68136 |
| [37] | Mobasher, B. and Pigozzi, D. and Slutzki, G. (1997a). Algebraic semantics for knowledge-based logic programs, In L. V. S. Lakshmanan and M. Nivat (Eds.), \(Proceedings international workshop on uncertainty in databases and deductive systems\), Ithaca, New York, Switzerland, pp. 77-109. Elsevier. · Zbl 0874.68046 |
| [38] | Mobasher, B. and Pigozzi, D. and Slutzki, G. (1997b). Multi-valued logic programming semantics: an algebraic approach, \(Theoretical Computer Science\)171(1-2), 77-109. · Zbl 0874.68046 |
| [39] | Mobasher, B. and Pigozzi, D. and Slutzki, G. and Voutsadakis, G. (2000). A duality theory for bilattices, \(Algebra Universalis\)43, 109-125. · Zbl 1012.06008 |
| [40] | Paƚasińska, K. and Pigozzi, D. (1995a). Gentzen-style axiomatizations in equational logic, \(Algebra Universalis\)34, 128-143. · Zbl 0831.08002 |
| [41] | Paƚasińska, K. and Pigozzi, D. (1995b, November). Implication in abstract algebra, Preprint 311, Centre de Recerca Matemàtica, Bellaterra (Spain). |
| [42] | Paƚasińska, K. and Pigozzi, D. (2000). Bikraty a programowanie logiczne oparte na wiedzy, In E. Szumakowicz (Ed.), \(Granice sztucznej inteligencji: eseje i studia\), pp. 179-211. Krak´ow: Politechnika Krakowska. |
| [43] | Pigozzi, D. (1972a). Amalgamation, congruence-extension, and interpolation properties of algebras, \(Algebra Universalis\)1, 269-349. · Zbl 0236.02047 |
| [44] | Pigozzi, D. (1972b). On some operations on classes of algebras, \(Algebra Universalis\)2, 346-353. · Zbl 0272.08006 |
| [45] | Pigozzi, D. (1974). The join of equational theories, \(Colloquium Mathematicae,\)30, 15-25, Institute of Mathematics, Polish Academy of Sciences, 1974. · Zbl 0319.02037 |
| [46] | Pigozzi, D. (1975, March). Equational logic and equational classes of algebras, Technical Report CSD 123, Purdue University, Department of Computer Science. |
| [47] | Pigozzi, D. (1976a). Base undecidable properties of universal varieties, \(Algebra Universalis\)6, 193-223. · Zbl 0356.08005 |
| [48] | Pigozzi, D. (1976b). The universality of the variety of quasigroups, \(Journal of the Australian Mathematical Society,\)21, 193-223. · Zbl 0356.08005 |
| [49] | Pigozzi, D. (1979a). Minimal, locally finite varieties that are not finitely axiomatizable, \(Algebra Universalis\)9, 374-390. · Zbl 0426.08003 |
| [50] | Pigozzi, D. (1979b). Universal equational theories and varieties of algebras, \(Annals of Mathematical Logic,\)17, 117-150. · Zbl 0436.03021 |
| [51] | Pigozzi, D. (1980). Varieties of pseudo-Post algebras, In \(The Tenth International Symposium on Multiple-valued Logic, Northwestern University, Evanston, Ill., 1980\), pp. 205. IEEE. · Zbl 0539.03047 |
| [52] | Pigozzi, D. (1981a). Finite groupoids without finite bases for their identities, \(Algebra Universalis\)13(1), 329-354. · Zbl 0475.08005 |
| [53] | Pigozzi, D. (1981b). On the structure of equationally complete varieties. I, \(Colloquium Mathematicae\)45:191-201. Institute of Mathematics, Polish Academy of Sciences. · Zbl 0492.08005 |
| [54] | Pigozzi, D. (1981c). On the structure of equationally complete varieties. II, \(Transactions of the American Mathematical Society\)264(2), 301-319. · Zbl 0492.08006 |
| [55] | Pigozzi, D. (1988a). Finite basis theorems for relatively congruencedistributive quasivarieties, \(Transactions of the American Mathematical Society\)310(2), 499-533. · Zbl 0706.08009 |
| [56] | Pigozzi, D. (1988b). Fregean algebraic logic, In J. D. Andréka, H. Monk and I. Németi (Eds.), \(Algebraic Logic\), Number 54 in Colloquia Mathematica Societatis, János Bolyai, pp. 473-502. Amsterdam: North-Holland. · Zbl 0749.03055 |
| [57] | Pigozzi, D. (1990). Data types over multiple-valued logics, \(Theoretical Computer Science\)77(1-2), 161-194. · Zbl 0716.03012 |
| [58] | Pigozzi, Don (1991). Equality-test and if-then-else algebras: Axiomatization and specification, \(SIAM Journal on Computing\)20(4), 766-805. · Zbl 0736.68061 |
| [59] | Pigozzi, D. (1992). A lattice theoretic characterization of equivalent quasivarieties, In O. H. K. L. A. Bokut, Yu. L. Ershov and A. I. Kostríkin (Eds.), \(Proceedings of the international conference on algebra honoring A. Mal’cev (Part 3)\), Volume 131 of \(Contempory Mathematics\), pp. 187-199. · Zbl 0760.08006 |
| [60] | Pigozzi, D. (1997a, May, June). Lectures in abstract algebraic logic (Draft), Elaboration of notes for a short couse taught at the Department of Mathematics, Univesity of Siena. |
| [61] | Pigozzi, D. (1997b, June). Second-order algebraizable logics (Draft), Centre de Recerca Matemàtica, Bellaterra (Spain). |
| [62] | Pigozzi, D. (1998, July). Abstract algebraic logic: past, present and future, In \(Workshop on Abstract Algebraic Logic\), Number 10, pp. 122-139. Bellaterra (Spain): Centre de Recerca Matemàtica. |
| [63] | Pigozzi, D. (1999a). Abstract algebraic logic, In A. M. Haeberer (Ed.), \(Algebraic methods and software technology\), Volume 1548 of \(Lecture Notes in Computer Science\), pp. 8-16. Proceedings 7th International Conference, AMAST’98 Amazonia, Brazil, January 1999: Springer, Verlag. · Zbl 0927.03085 |
| [64] | Pigozzi, D. (1999b, May). Abstract algebraic logic and the specification of abstract data types (Draft), A course of lectures, Center for Algebra, University of Lisbon. |
| [65] | Pigozzi, Don (2002). Abstract algebraic logic, in M. Hazewinkel, editor, \(Encyklopaedia of Mathematics, Supplement III\), volume 13 of \(Encyklopaedia of Mathematics\), Chapter A, pp. 2-13, Springer Netherlands. |
| [66] | Pigozzi, D. (2004, July 28-30). Combining interpreted languages in abstract algebraic logic, In W. A. Carnielli, F. M. Dion˜Asio, and P. Mateus (Eds.), \(CombLog’04, Workshop on Combination of Logics: Theory and Applications\). CLC, Department of Mathematics, IST, Lisbon, Portugal. |
| [67] | Pigozzi, D. and Salibra, A. (1993a). An introduction to lambda abstraction algebras, In \(IX Simposio Latinoamericano de Logica Matematica\), Volume 38, pp. 93-112. Universidad Nacional del Sur Bahia Bianca, Argentina. · Zbl 0820.03039 |
| [68] | Pigozzi, D. and Salibra, A. (1993b). Polyadic algebras over nonclassical logics, in \(Algebraic ¡ethods in Logic and in Computer Science\), volume 28 of \(Banach Center Publications\), pp. 51-66, Warszawa, Institute of Polish Academy of Sciences. · Zbl 0794.03092 |
| [69] | Pigozzi, D. and Salibra, A. (1993c). A representation theorem for lambda abstraction algebras, In A. M. Borzyszkowski and S. Sokolowski (Eds.), \(Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science\), Volume 7111 of \(Lecture Notes in Computer Science\), pp. 629-639. Springer-Verlag. · Zbl 0925.03087 |
| [70] | Pigozzi, D. and Salibra, A. (1994). Dimension-complemented lambda abstraction algebras, In T. R. M. Nivat, C. Rattray and G. Scollo (Eds.), \(Algebraic Methodology and Software Technology (AMAST’93)\), Workshops in Computing, pp. 129-136. Springer-Verlag. |
| [71] | Pigozzi, D. and Salibra, A. (1995a). The abstract variable-binding calculus, \(Studia Logica\)55(1), 129-179. · Zbl 0836.03038 |
| [72] | Pigozzi, D. and Salibra, A. (1995). Lambda abstraction algebras: representation theorems, \(Theoretical Computer Science\)140(1), 5-52. · Zbl 0874.68188 |
| [73] | Pigozzi, D. and Salibra, A. (1998). Lambda abstraction algebras: coordinatizing models of lambda calculus, \(Fundamenta Informaticae\)33(2), 149-200. · Zbl 0909.03018 |
| [74] | Pigozzi, D. and Sichler, J. (1985). Homomorphisms of partial and of complete steiner triple systems and quasigroups, In \(Universal algebra and lattice theory\), Volume 1149 of \(Lecture Notes In Mathematics\), pp. 224-237, Proceedings of Conference in Universal Algebra, Charleston, South Carolina, July 11-14, 1984. · Zbl 0572.20057 |
| [75] | Pigozzi, D and Tardos, G. |
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