The Association for Symbolic Logic publishes analytical reviews of selected books and articles in the field of symbolic logic. The reviews were published in The Journal of Symbolic Logic from the founding of the Journal in 1936 until the end of 1999. The Association moved the reviews to this Bulletin, beginning in 2000. The Reviews Section is edited by Alasdair Urquhart (Managing Editor), Steve Awodey, John Baldwin, LevBeklemishev, Anuj Dawar,MirnaDžamonja, David Evans, ErichGrädel, Denis Hirschfeldt, Hannes Leitgeb, Roger Maddux, Grigori Mints, and Volker Peckhaus. Authors and publishers are requested to send, for review, copies of books to ASL, Box 742, Vassar College, 124 Raymond Avenue, Poughkeepsie, NY 12604, USA. In a review, a reference “JSL XLIII 148,” for example, refers either to the publication reviewed on page 148 of volume 43 of the Journal, or to the review itself (which contains full bibliographical information for the reviewed publication). Analogously, a reference “BSL VII 376” refers to the review beginning on page 376 in volume 7 of this Bulletin, or to the publication there reviewed. “JSL LV 347” refers to one of the reviews or one of the publications reviewed or listed on page 347 of volume 55 of the Journal, with reliance on the context to show which one is meant. The reference “JSL LIII 318(3)” is to the third item on page 318 of volume 53 of the Journal, that is, to van Heijenoort’s Frege and vagueness, and “JSL LX 684(8)” refers to the eighth item on page 684 of volume 60 of the Journal, that is, to Tarski’s Truth and proof. References such as 495 or 2801 are to entries so numbered in A bibliography of symbolic logic (the Journal, vol. 1, pp. 121–218).
{"title":"Absolute generality , edited by Agustín Rayo and Gabriel Uzquiano, Clarendon Press, Oxford, 2006, ix + 396 pp.","authors":"Philip Smith","doi":"10.2178/BSL/1231081373","DOIUrl":"https://doi.org/10.2178/BSL/1231081373","url":null,"abstract":"The Association for Symbolic Logic publishes analytical reviews of selected books and articles in the field of symbolic logic. The reviews were published in The Journal of Symbolic Logic from the founding of the Journal in 1936 until the end of 1999. The Association moved the reviews to this Bulletin, beginning in 2000. The Reviews Section is edited by Alasdair Urquhart (Managing Editor), Steve Awodey, John Baldwin, LevBeklemishev, Anuj Dawar,MirnaDžamonja, David Evans, ErichGrädel, Denis Hirschfeldt, Hannes Leitgeb, Roger Maddux, Grigori Mints, and Volker Peckhaus. Authors and publishers are requested to send, for review, copies of books to ASL, Box 742, Vassar College, 124 Raymond Avenue, Poughkeepsie, NY 12604, USA. In a review, a reference “JSL XLIII 148,” for example, refers either to the publication reviewed on page 148 of volume 43 of the Journal, or to the review itself (which contains full bibliographical information for the reviewed publication). Analogously, a reference “BSL VII 376” refers to the review beginning on page 376 in volume 7 of this Bulletin, or to the publication there reviewed. “JSL LV 347” refers to one of the reviews or one of the publications reviewed or listed on page 347 of volume 55 of the Journal, with reliance on the context to show which one is meant. The reference “JSL LIII 318(3)” is to the third item on page 318 of volume 53 of the Journal, that is, to van Heijenoort’s Frege and vagueness, and “JSL LX 684(8)” refers to the eighth item on page 684 of volume 60 of the Journal, that is, to Tarski’s Truth and proof. References such as 495 or 2801 are to entries so numbered in A bibliography of symbolic logic (the Journal, vol. 1, pp. 121–218).","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"398 - 401"},"PeriodicalIF":0.6,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2178/BSL/1231081373","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68346858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This brief article is intended to introduce the reader to the field of algebraic set theory, in which models of set theory of a new and fascinating kind are determined algebraically. The method is quite robust, applying to various classical, intuitionistic, and constructive set theories. Under this scheme some familiar set theoretic properties are related to algebraic ones, while others result from logical constraints. Conventional elementary set theories are complete with respect to algebraic models, which arise in a variety of ways, such as topologically, type-theoretically, and through variation. Many previous results from topos theory involving realizability, permutation, and sheaf models of set theory are subsumed, and the prospects for further such unification seem bright.
{"title":"A Brief Introduction to Algebraic Set Theory","authors":"S. Awodey","doi":"10.2178/bsl/1231081369","DOIUrl":"https://doi.org/10.2178/bsl/1231081369","url":null,"abstract":"Abstract This brief article is intended to introduce the reader to the field of algebraic set theory, in which models of set theory of a new and fascinating kind are determined algebraically. The method is quite robust, applying to various classical, intuitionistic, and constructive set theories. Under this scheme some familiar set theoretic properties are related to algebraic ones, while others result from logical constraints. Conventional elementary set theories are complete with respect to algebraic models, which arise in a variety of ways, such as topologically, type-theoretically, and through variation. Many previous results from topos theory involving realizability, permutation, and sheaf models of set theory are subsumed, and the prospects for further such unification seem bright.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"281 - 298"},"PeriodicalIF":0.6,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2178/bsl/1231081369","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68346483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-06-01DOI: 10.1017/S1079898600001724
Robert S. Lubarsky
{"title":"Rudolf Taschner. The Continuum . Friedrich Vieweg & Sohn Verlag, Wiesbaden, Germany, 2005, 136 pp.","authors":"Robert S. Lubarsky","doi":"10.1017/S1079898600001724","DOIUrl":"https://doi.org/10.1017/S1079898600001724","url":null,"abstract":"","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"260 - 262"},"PeriodicalIF":0.6,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S1079898600001724","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57302836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The last decade has seen an enormous development in infinite-valued systems and in particular in such systems which have become known as mathematical fuzzy logics. The paper discusses the mathematical background for the interest in such systems of mathematical fuzzy logics, as well as the most important ones of them. It concentrates on the propositional cases, and mentions the first-order systems more superficially. The main ideas, however, become clear already in this restricted setting.
{"title":"Mathematical Fuzzy Logics","authors":"S. Gottwald","doi":"10.2178/bsl/1208442828","DOIUrl":"https://doi.org/10.2178/bsl/1208442828","url":null,"abstract":"Abstract The last decade has seen an enormous development in infinite-valued systems and in particular in such systems which have become known as mathematical fuzzy logics. The paper discusses the mathematical background for the interest in such systems of mathematical fuzzy logics, as well as the most important ones of them. It concentrates on the propositional cases, and mentions the first-order systems more superficially. The main ideas, however, become clear already in this restricted setting.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"210 - 239"},"PeriodicalIF":0.6,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2178/bsl/1208442828","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68346253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A structure has a (finite-string) automatic presentation if the elements of its domain can be named by finite strings in such a way that the coded domain and the coded atomic operations are recognised by synchronous multitape automata. Consequently, every structure with an automatic presentation has a decidable first-order theory. The problems surveyed here include the classification of classes of structures with automatic presentations, the complexity of the isomorphism problem, and the relationship between definability and recognisability.
{"title":"Automata Presenting Structures: A Survey of the Finite String Case","authors":"S. Rubin","doi":"10.2178/bsl/1208442827","DOIUrl":"https://doi.org/10.2178/bsl/1208442827","url":null,"abstract":"Abstract A structure has a (finite-string) automatic presentation if the elements of its domain can be named by finite strings in such a way that the coded domain and the coded atomic operations are recognised by synchronous multitape automata. Consequently, every structure with an automatic presentation has a decidable first-order theory. The problems surveyed here include the classification of classes of structures with automatic presentations, the complexity of the isomorphism problem, and the relationship between definability and recognisability.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"169 - 209"},"PeriodicalIF":0.6,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2178/bsl/1208442827","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68346607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-06-01DOI: 10.1017/S1079898600001761
Lutz Straßburger
also suggests a non-standard syllogistics with restricted quantifiers, using a symbolism like “C 2 is B” standing for “I know only with half certainty that C is B”. The central piece is the famous “Sammlung der Schriften, welche den logischen Calcul Herrn Prof. Ploucquet’s betreffen, mit neuen Zusätzen” (Collection of writings concerning Professor Ploucquet’s logical calculus, with new additions) (pp. 37–316), first published by August Friedrich Bök in 1766. It contains the documents of an argument about the qualities of Lambert’s line calculus in comparison with the geometrical calculus of Gottfried Ploucquet, professor of philosophy in Tübingen, who used rectangulars on the basis of an identity theory of judgements. Further contributions by Heinrich Wilhelm Clemm and Georg Jonathan Holland are included in this collection. A short tract “De universaliori calculi idea disquisitio una cum adnexo specimine” (pp. 327–359) first published in Nova acta eruditorum (1765) explicitly extends the Leibnizian idea of a universal calculus. Lambert suggests a calculus of properties and qualities using algebraic symbols for logical operations and relations. It is Lambert’s only publication on calculi of intensions. His “Sechs Versuche einer Zeichenkunst in der Vernunftlehre” (Six attempts of an art of characters in a theory of reason) appeared posthumously (see vol. VI of the Philosophische Schriften). Considerations on a characteristic art and its application to different fields are taken up in other papers like “In algebram philosophicam cl. Richeri breves adnotationes” (pp. 361– 372) or “Observations sur quelques dimensions du monde intellectuel” (pp. 373–390) with an application to esthetics. Partial volume 2 is devoted to Lambert’s reviews published in the Allgemeine Deutsche Bibliothek between 1768 and 1777, among them several comments on works on logic. An index of the books reviewed makes access easier. This edition provides facsimile reprints of the texts. A comprehensive introduction gives useful information on the background and summaries of the material edited. This important edition of Lambert’s philosophical works will be finished in 2008 with volume X, containing further philosophical writings, drafts and reviews with new material from the Nachlass. The edition provides a reliable textual basis for investigating the philosophical ideas of this major figure in European enlightenment who wrote in Leibnizian spirit. Volker Peckhaus Universität Paderborn, Institut für Humanwissenschaften: Philosophie, Warburger Str. 100, D-33098 Paderborn, Germany. volker.peckhaus@upb.de.
他还提出了一种非标准的三段论，带有限制性的量词，使用像“c2是B”这样的符号来代表“我只有一半的把握知道C是B”。中心部分是著名的“Sammlung der Schriften, welche den logischen Calcul Herrn教授Ploucquet 's betreffen, mit neuen Zusätzen”(关于Ploucquet教授的逻辑演绎法的文集，新添加)(第37-316页)，由August Friedrich于1766年首次出版Bök。它包含了关于兰伯特直线微积分与格特弗里德·普劳凯(Gottfried Ploucquet)几何微积分的性质的争论文件，普劳凯是宾根大学的哲学教授，他在判断的同一性理论的基础上使用了矩形。海因里希·威廉·克莱姆和乔治·乔纳森·霍兰德的进一步贡献包括在这个集合中。1765年发表在《新星学报》(Nova acta eruditorum)上的一篇短文“De universaliori calculus idea disquisitio una cum adnexo speciine”(第327-359页)明确地扩展了莱布尼兹关于普遍微积分的思想。兰伯特建议用代数符号来表示逻辑运算和关系的性质和性质的演算。这是兰伯特唯一一本关于内涵演算的著作。他的《理性理论中人物艺术的六种尝试》(Sechs Versuche einer Zeichenkunst in der Vernunftlehre)是在他死后发表的(见《哲学史册》第六卷)。关于一门特色艺术及其在不同领域的应用的考虑，在其他论文中也有，如“代数哲学”。里切里将“注释”(第361 - 372页)或“对世界智力维度的观察”(第373-390页)应用于美学。第二卷的部分内容是兰伯特在1768年至1777年间发表在《德意志总文献》上的评论，其中有几篇对逻辑学著作的评论。书评的索引使查阅更容易。这个版本提供了文本的复印版。一个全面的介绍提供了有用的信息的背景和摘要的材料编辑。兰伯特哲学著作的这一重要版本将于2008年完成第十卷，其中包含了进一步的哲学著作、草稿和对Nachlass新材料的评论。该版本为研究这位以莱布尼茨精神写作的欧洲启蒙运动主要人物的哲学思想提供了可靠的文本基础。Volker Peckhaus Universität帕德伯恩，人类智慧与哲学研究所，德国帕德伯恩，华堡街100号，D-33098。volker.peckhaus@upb.de。
{"title":"Kosta Došen and Zoran Petrić. Proof-net categories . Polymetrica International Scientific Publisher, Monza, Italy, 2007, viii + 147 pp.","authors":"Lutz Straßburger","doi":"10.1017/S1079898600001761","DOIUrl":"https://doi.org/10.1017/S1079898600001761","url":null,"abstract":"also suggests a non-standard syllogistics with restricted quantifiers, using a symbolism like “C 2 is B” standing for “I know only with half certainty that C is B”. The central piece is the famous “Sammlung der Schriften, welche den logischen Calcul Herrn Prof. Ploucquet’s betreffen, mit neuen Zusätzen” (Collection of writings concerning Professor Ploucquet’s logical calculus, with new additions) (pp. 37–316), first published by August Friedrich Bök in 1766. It contains the documents of an argument about the qualities of Lambert’s line calculus in comparison with the geometrical calculus of Gottfried Ploucquet, professor of philosophy in Tübingen, who used rectangulars on the basis of an identity theory of judgements. Further contributions by Heinrich Wilhelm Clemm and Georg Jonathan Holland are included in this collection. A short tract “De universaliori calculi idea disquisitio una cum adnexo specimine” (pp. 327–359) first published in Nova acta eruditorum (1765) explicitly extends the Leibnizian idea of a universal calculus. Lambert suggests a calculus of properties and qualities using algebraic symbols for logical operations and relations. It is Lambert’s only publication on calculi of intensions. His “Sechs Versuche einer Zeichenkunst in der Vernunftlehre” (Six attempts of an art of characters in a theory of reason) appeared posthumously (see vol. VI of the Philosophische Schriften). Considerations on a characteristic art and its application to different fields are taken up in other papers like “In algebram philosophicam cl. Richeri breves adnotationes” (pp. 361– 372) or “Observations sur quelques dimensions du monde intellectuel” (pp. 373–390) with an application to esthetics. Partial volume 2 is devoted to Lambert’s reviews published in the Allgemeine Deutsche Bibliothek between 1768 and 1777, among them several comments on works on logic. An index of the books reviewed makes access easier. This edition provides facsimile reprints of the texts. A comprehensive introduction gives useful information on the background and summaries of the material edited. This important edition of Lambert’s philosophical works will be finished in 2008 with volume X, containing further philosophical writings, drafts and reviews with new material from the Nachlass. The edition provides a reliable textual basis for investigating the philosophical ideas of this major figure in European enlightenment who wrote in Leibnizian spirit. Volker Peckhaus Universität Paderborn, Institut für Humanwissenschaften: Philosophie, Warburger Str. 100, D-33098 Paderborn, Germany. volker.peckhaus@upb.de.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"268 - 271"},"PeriodicalIF":0.6,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S1079898600001761","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57302696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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