纪念:j .迈克尔·邓恩,1941-2021

K. Bimbó
{"title":"纪念:j .迈克尔·邓恩,1941-2021","authors":"K. Bimbó","doi":"10.1017/bsl.2021.65","DOIUrl":null,"url":null,"abstract":"The history of relevance logic cannot be written without mentioning J. Michael Dunn who played a prominent role in shaping this area of logic. In the late twentieth century, he was a doyen with a world-class reputation in the field of philosophical logic. Dunn’s research also encompassed logics outside of relevance logic, from 2-valued first-order logic to quantum logic and substructural logics such as the Lambek calculi, intuitionistic logic, linear logic, etc. Each of the disciplines of philosophy, mathematics, and computer science has been impacted in intrinsic ways by some of the theorems proved by Dunn. Jon Michael Dunn was born in Fort Wayne, Indiana, on June 19, 1941, and he passed away on April 5, 2021, in Bloomington, Indiana. After attending high schools in Fort Wayne and Lafayette, he obtained an AB degree in philosophy from Oberlin College, Ohio, in 1963. Dunn completed his Ph.D. Thesis entitled The Algebra of Intensional Logics at Pittsburgh University in 1966; his thesis supervisor was Nuel D. Belnap. In 1969, Dunn was appointed an associate professor in the Department of Philosophy at Indiana University in Bloomington, Indiana, and he stayed on the faculty at IU until 2007, when he retired as University Dean of the School of Informatics, Oscar R. Ewing Professor of Philosophy, Professor of Informatics, Professor of Computer Science, and Core Faculty in Cognitive Science. Dunn supervised 14 Ph.D. students in logic and 3 Ph.D. students in other areas of philosophy. He taught advanced graduate courses in logic, including courses on 2-valued logic (metalogic), modal logic, algebraic logics, and substructural logics. Dunn was the founding dean of the School of Informatics, and he served in other administrative positions such as Chair of the Department of Philosophy and Associate Dean of the College of Arts and Sciences in previous years. Dunn held multiple research grants and visiting positions at universities in the US, Europe, and Australia. Dunn, for his contributions to Indiana University, was honored by the IU Provost Medallion in 2007. The state of Indiana bestowed on Dunn the rank and title of Sagamore of the Wabash the same year. Dunn was elected a Fellow of the American Academy of Arts and Sciences in 2010. The logic of relevant implication R combines Church’s “weak implication” with lattice connectives and De Morgan negation. Alternatively, R results from Ackermann’s system Π′ by omitting a rule (the so-called rule) and adding permutation. Dunn started to investigate R from an algebraic point of view in his Ph.D. thesis [14]. This research continued the study of distributive lattices with De Morgan negation already underway in [1, 4, 5, 35, 43]. Dunn showed that 4, the four-element lattice with two incomparable elements on which negation has fixed points, plays a fundamental role among De Morgan lattices, and hence, for first-degree entailments fde; (the implication-free fragment of R and of the logic of entailment E). Dunn proved—using methods similar to those Stone utilized in his representation of Boolean algebras—that every De Morgan lattice is embeddable into a product of 4, that is, into ∏ i<κ 4i , where κ ≤ 2 and is the cardinality of the De Morgan lattice. Whenever possible, Dunn generalized theorems to complete lattices, complete homomorphisms, complete embeddings, and similar notions, which, strictly speaking, go beyond the purely algebraic approach. He also defined a new interpretation for fde that relies on pairs of sets of situations. Later, Dunn defined the four values (true, false, both, and neither) that emerge in the interpretation of fde as subsets of {T, F }, and Belnap provided motivations for these values by appeal to databases. Nowadays, this logic is often referred to as Dunn–Belnap (or Belnap–Dunn) logic (cf. [48]). The algebraization of R revolves around two concepts: residuation and the intensional truth constant (denoted by t). Relevant","PeriodicalId":22265,"journal":{"name":"The Bulletin of Symbolic Logic","volume":"54 1","pages":"519 - 525"},"PeriodicalIF":0.0000,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"IN MEMORIAM: J. MICHAEL DUNN, 1941–2021\",\"authors\":\"K. Bimbó\",\"doi\":\"10.1017/bsl.2021.65\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The history of relevance logic cannot be written without mentioning J. Michael Dunn who played a prominent role in shaping this area of logic. In the late twentieth century, he was a doyen with a world-class reputation in the field of philosophical logic. Dunn’s research also encompassed logics outside of relevance logic, from 2-valued first-order logic to quantum logic and substructural logics such as the Lambek calculi, intuitionistic logic, linear logic, etc. Each of the disciplines of philosophy, mathematics, and computer science has been impacted in intrinsic ways by some of the theorems proved by Dunn. Jon Michael Dunn was born in Fort Wayne, Indiana, on June 19, 1941, and he passed away on April 5, 2021, in Bloomington, Indiana. After attending high schools in Fort Wayne and Lafayette, he obtained an AB degree in philosophy from Oberlin College, Ohio, in 1963. Dunn completed his Ph.D. Thesis entitled The Algebra of Intensional Logics at Pittsburgh University in 1966; his thesis supervisor was Nuel D. Belnap. In 1969, Dunn was appointed an associate professor in the Department of Philosophy at Indiana University in Bloomington, Indiana, and he stayed on the faculty at IU until 2007, when he retired as University Dean of the School of Informatics, Oscar R. Ewing Professor of Philosophy, Professor of Informatics, Professor of Computer Science, and Core Faculty in Cognitive Science. Dunn supervised 14 Ph.D. students in logic and 3 Ph.D. students in other areas of philosophy. He taught advanced graduate courses in logic, including courses on 2-valued logic (metalogic), modal logic, algebraic logics, and substructural logics. Dunn was the founding dean of the School of Informatics, and he served in other administrative positions such as Chair of the Department of Philosophy and Associate Dean of the College of Arts and Sciences in previous years. Dunn held multiple research grants and visiting positions at universities in the US, Europe, and Australia. Dunn, for his contributions to Indiana University, was honored by the IU Provost Medallion in 2007. The state of Indiana bestowed on Dunn the rank and title of Sagamore of the Wabash the same year. Dunn was elected a Fellow of the American Academy of Arts and Sciences in 2010. The logic of relevant implication R combines Church’s “weak implication” with lattice connectives and De Morgan negation. Alternatively, R results from Ackermann’s system Π′ by omitting a rule (the so-called rule) and adding permutation. Dunn started to investigate R from an algebraic point of view in his Ph.D. thesis [14]. This research continued the study of distributive lattices with De Morgan negation already underway in [1, 4, 5, 35, 43]. Dunn showed that 4, the four-element lattice with two incomparable elements on which negation has fixed points, plays a fundamental role among De Morgan lattices, and hence, for first-degree entailments fde; (the implication-free fragment of R and of the logic of entailment E). Dunn proved—using methods similar to those Stone utilized in his representation of Boolean algebras—that every De Morgan lattice is embeddable into a product of 4, that is, into ∏ i<κ 4i , where κ ≤ 2 and is the cardinality of the De Morgan lattice. Whenever possible, Dunn generalized theorems to complete lattices, complete homomorphisms, complete embeddings, and similar notions, which, strictly speaking, go beyond the purely algebraic approach. He also defined a new interpretation for fde that relies on pairs of sets of situations. Later, Dunn defined the four values (true, false, both, and neither) that emerge in the interpretation of fde as subsets of {T, F }, and Belnap provided motivations for these values by appeal to databases. Nowadays, this logic is often referred to as Dunn–Belnap (or Belnap–Dunn) logic (cf. [48]). The algebraization of R revolves around two concepts: residuation and the intensional truth constant (denoted by t). Relevant\",\"PeriodicalId\":22265,\"journal\":{\"name\":\"The Bulletin of Symbolic Logic\",\"volume\":\"54 1\",\"pages\":\"519 - 525\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Bulletin of Symbolic Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/bsl.2021.65\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Bulletin of Symbolic Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/bsl.2021.65","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

关联逻辑的历史不能不提到J. Michael Dunn,他在塑造这一逻辑领域方面发挥了突出作用。在二十世纪后期,他是哲学逻辑领域中享有世界级声誉的元老。Dunn的研究还涵盖了关联逻辑之外的逻辑,从2值一阶逻辑到量子逻辑和子结构逻辑,如Lambek演算、直觉逻辑、线性逻辑等。哲学、数学和计算机科学的每一个学科都在本质上受到邓恩所证明的一些定理的影响。乔恩·迈克尔·邓恩1941年6月19日出生在印第安纳州的韦恩堡,2021年4月5日在印第安纳州的布卢明顿去世。在韦恩堡和拉斐特读完高中后,他于1963年在俄亥俄州奥伯林学院获得了哲学学士学位。1966年,邓恩在匹兹堡大学完成了他的博士论文《内涵逻辑的代数》;他的论文导师是努尔·贝尔纳普。1969年,邓恩被任命为印第安纳州布卢明顿市印第安纳大学哲学系副教授,并一直在印第安纳大学任教,直到2007年,当他从大学信息学学院院长、奥斯卡·r·尤因哲学教授、信息学教授、计算机科学教授和认知科学核心教员的职位上退休。邓恩指导了14名逻辑学博士生和3名其他哲学领域的博士生。他教授高级研究生逻辑学课程,包括2值逻辑(元逻辑)、模态逻辑、代数逻辑和子结构逻辑。Dunn是信息学学院的创始院长,他曾担任其他行政职位,如哲学系主席和艺术与科学学院副院长。邓恩曾在美国、欧洲和澳大利亚的多所大学获得多项研究资助和访问职位。邓恩因其对印第安纳大学的贡献,于2007年被授予印第安纳大学教务长奖章。同年,印第安纳州授予邓恩“沃巴什的萨加莫尔”的称号。Dunn于2010年当选为美国艺术与科学院院士。相关蕴涵R的逻辑结合了丘奇的“弱蕴涵”与格连接词和De Morgan否定。或者,R是通过Ackermann的系统Π '通过省略规则(所谓的规则)和添加排列而得到的。Dunn在博士论文中开始从代数的角度研究R[14]。本研究继续对De Morgan否定的分布格进行了研究[1,4,5,35,43]。Dunn证明了4,具有两个不可比较的元素的四元格,其否定有不动点,在De Morgan格中起着基本的作用,因此,对于De的一级蕴涵;(R的无隐含片段和蕴涵E的逻辑)。邓恩证明-使用类似于斯通在布尔代数表示中使用的方法-每个德摩根晶格都可嵌入到一个4的乘积中,即∏i<κ 4i,其中κ≤2并且是德摩根晶格的cardinality。只要有可能,邓恩将定理推广到完全格、完全同态、完全嵌入和类似的概念,严格地说,这超越了纯粹的代数方法。他还为fde定义了一种新的解释,这种解释依赖于成对的情况集。后来,Dunn定义了四个值(true, false, both和neither),这些值出现在fde的解释中,作为{T, F}的子集,而Belnap通过诉诸数据库为这些值提供了动机。现在,这种逻辑通常被称为Dunn-Belnap(或Belnap-Dunn)逻辑(参见[48])。R的代数化围绕着两个概念:残数和内涵真值常数(用t表示)。相关
本文章由计算机程序翻译,如有差异,请以英文原文为准。
IN MEMORIAM: J. MICHAEL DUNN, 1941–2021
The history of relevance logic cannot be written without mentioning J. Michael Dunn who played a prominent role in shaping this area of logic. In the late twentieth century, he was a doyen with a world-class reputation in the field of philosophical logic. Dunn’s research also encompassed logics outside of relevance logic, from 2-valued first-order logic to quantum logic and substructural logics such as the Lambek calculi, intuitionistic logic, linear logic, etc. Each of the disciplines of philosophy, mathematics, and computer science has been impacted in intrinsic ways by some of the theorems proved by Dunn. Jon Michael Dunn was born in Fort Wayne, Indiana, on June 19, 1941, and he passed away on April 5, 2021, in Bloomington, Indiana. After attending high schools in Fort Wayne and Lafayette, he obtained an AB degree in philosophy from Oberlin College, Ohio, in 1963. Dunn completed his Ph.D. Thesis entitled The Algebra of Intensional Logics at Pittsburgh University in 1966; his thesis supervisor was Nuel D. Belnap. In 1969, Dunn was appointed an associate professor in the Department of Philosophy at Indiana University in Bloomington, Indiana, and he stayed on the faculty at IU until 2007, when he retired as University Dean of the School of Informatics, Oscar R. Ewing Professor of Philosophy, Professor of Informatics, Professor of Computer Science, and Core Faculty in Cognitive Science. Dunn supervised 14 Ph.D. students in logic and 3 Ph.D. students in other areas of philosophy. He taught advanced graduate courses in logic, including courses on 2-valued logic (metalogic), modal logic, algebraic logics, and substructural logics. Dunn was the founding dean of the School of Informatics, and he served in other administrative positions such as Chair of the Department of Philosophy and Associate Dean of the College of Arts and Sciences in previous years. Dunn held multiple research grants and visiting positions at universities in the US, Europe, and Australia. Dunn, for his contributions to Indiana University, was honored by the IU Provost Medallion in 2007. The state of Indiana bestowed on Dunn the rank and title of Sagamore of the Wabash the same year. Dunn was elected a Fellow of the American Academy of Arts and Sciences in 2010. The logic of relevant implication R combines Church’s “weak implication” with lattice connectives and De Morgan negation. Alternatively, R results from Ackermann’s system Π′ by omitting a rule (the so-called rule) and adding permutation. Dunn started to investigate R from an algebraic point of view in his Ph.D. thesis [14]. This research continued the study of distributive lattices with De Morgan negation already underway in [1, 4, 5, 35, 43]. Dunn showed that 4, the four-element lattice with two incomparable elements on which negation has fixed points, plays a fundamental role among De Morgan lattices, and hence, for first-degree entailments fde; (the implication-free fragment of R and of the logic of entailment E). Dunn proved—using methods similar to those Stone utilized in his representation of Boolean algebras—that every De Morgan lattice is embeddable into a product of 4, that is, into ∏ i<κ 4i , where κ ≤ 2 and is the cardinality of the De Morgan lattice. Whenever possible, Dunn generalized theorems to complete lattices, complete homomorphisms, complete embeddings, and similar notions, which, strictly speaking, go beyond the purely algebraic approach. He also defined a new interpretation for fde that relies on pairs of sets of situations. Later, Dunn defined the four values (true, false, both, and neither) that emerge in the interpretation of fde as subsets of {T, F }, and Belnap provided motivations for these values by appeal to databases. Nowadays, this logic is often referred to as Dunn–Belnap (or Belnap–Dunn) logic (cf. [48]). The algebraization of R revolves around two concepts: residuation and the intensional truth constant (denoted by t). Relevant
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