Bulletin of Symbolic Logic最新文献

{"title":"Current topics in logic and analytic philosophy. edited by Concha Martínez, José L. Falguera and José M. Sagüillo, Colloquium on Logic and Analytic Philosophy at Santiago de Compostela, 2001–2005. Universidade de Santiago de Compostela, 2007, 288 pp.","authors":"A. Urquhart","doi":"10.1017/S1079898600001773","DOIUrl":"https://doi.org/10.1017/S1079898600001773","url":null,"abstract":"Finally, the sentence “The notion of proof net is not decidable in an elementary way” (p. 131) is plain wrong. A proof net consists of a sequence of formulas, equipped with the axiom links (i.e., the coherence graph). The question whether such an object is correct, (i.e., represents an actual proof) can be decided in linear time. Lutz Strassburger École Polytechnique, LIX, Rue de Saclay, 91128 Palaiseau Cedex, France Lutz.Strassburger@inria.fr.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"271 - 272"},"PeriodicalIF":0.6,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S1079898600001773","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57303171","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}

{"title":"Ian Chiswell and Wilfrid Hodges. Mathematical logic. Oxford Texts in Logic, vol. 3. Oxford University Press, Oxford, England, 2007, 250 pp.","authors":"Robert S. Lubarsky","doi":"10.1017/S1079898600001748","DOIUrl":"https://doi.org/10.1017/S1079898600001748","url":null,"abstract":"that expressions like ‘brother’ and ‘male sibling’ may be translated into the same expression of another language that has only one phrase for the concept while preserving sense. Salmon proposses to resolve the conflict by abandoning Church’s solution to the paradox, noting that doing so appears to undermine the original impetus behind Frege’s distinction between Sinn and Bedeutung. The very possibility of language also discusses Church’s Translation Argument, arguing that the moral of that argument shows that Dummett’s account of language collapses into the absurd position that it is impossible for us to know a language. The volume contain a helpful bibliography of Salmon’s writings from1979–2005. Unfortunately, there is no bibliography of the works cited; the details are included only in footnotes. There is a good deal of cross-referencing amongst the included papers; regrettably, these references refer to other papers that appear in the collection by their original pagination. Furthermore, cross-references to footnotes internal to an individual paper seem not always to have been updated when changes to the text affected the numbering of the notes. The text is well bound, attractively if densely type-set, and relatively free from typographical errors. Happily, those that exist are easily rectified. Brian van den Broek Department of Philosophy, University of Manitoba, Winnipeg, Manitoba, R3T 2M8, Canada. broek@cc.umanitoba.ca.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"265 - 267"},"PeriodicalIF":0.6,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S1079898600001748","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57302896","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}

{"title":"Gentzen's Proof of Normalization for Natural Deduction","authors":"Jan von Plato","doi":"10.2178/bsl/1208442829","DOIUrl":"https://doi.org/10.2178/bsl/1208442829","url":null,"abstract":"Abstract Gentzen writes in the published version of his doctoral thesis Untersuchungen über das logische Schliessen (Investigations into logical reasoning) that he was able to prove the normalization theorem only for intuitionistic natural deduction, but not for classical. To cover the latter, he developed classical sequent calculus and proved a corresponding theorem, the famous cut elimination result. Its proof was organized so that a cut elimination result for an intuitionistic sequent calculus came out as a special case, namely the one in which the sequents have at most one formula in the right, succedent part. Thus, there was no need for a direct proof of normalization for intuitionistic natural deduction. The only traces of such a proof in the published thesis are some convertibilities, such as when an implication introduction is followed by an implication elimination [1934–35, II.5.13]. It remained to Dag Prawitz in 1965 to work out a proof of normalization. Another, less known proof was given also in 1965 by Andres Raggio. We found in February 2005 an early handwritten version of Gentzen's thesis, with exactly the above title, but with rather different contents: Most remarkably, it contains a detailed proof of normalization for what became the standard system of natural deduction. The manuscript is located in the Paul Bernays collection at the ETH-Zurichwith the signum Hs. 974: 271. Bernays must have gotten it well before the time of his being expelled from Göttingen on the basis of the racial laws in April 1933.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"240 - 257"},"PeriodicalIF":0.6,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2178/bsl/1208442829","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68346343","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}

{"title":"Johann Heinrich Lambert. Philosophische Schriften. Vol. VIII: Kleinere philosophische Abhandlungen und Rezensionen. edited by A. Emmel and A. Spree, Georg Olms Verlag, Hildesheim, Zurich and New York 2007, Part 1: xlii + pp. 1–474; Part 2: pp. 475–763.","authors":"V. Peckhaus","doi":"10.1017/S107989860000175X","DOIUrl":"https://doi.org/10.1017/S107989860000175X","url":null,"abstract":"They report the results, which include 0% getting the correct answer, and in the following discussion mention that their results are typical. The second interlude is the Linda problem. Linda is described (in more detail than this) as being socially concerned and left-leaning. Then eight statements (a)–(h) about Linda are listed, and the subject is asked to rank them in order of probability. Six are red herrings. The two of interest are: (f) Linda is a bank teller, and (h) Linda is a bank teller and is active in the feminist movement. Apparently the majority of participants rank (h) as more likely than (f), presumably because it contains some information more consistent with the overall image of Linda, even though (h) implies (f) whereas (f) does not imply (h). (The authors report that these two phenomena and variants have been intensely studied by psychologists. In fact, one of the researchers behind the latter test, Kahneman, was awarded the Nobel Memorial Prize in Economic Sciences in 2002 for this work, done with Tversky, who had by then passed away.) Another charm of the book are the many photographs of (or, if that is not possible, graphics related to) important figures in logic, with a snippet about their contribution to the field. In fact, the first chapter is just two pages devoted to five mathematicians from Euclid to Gentzen addressing the question as to what mathematics is (as well as a one-page pronunciation guide). Along the way we also meet de Morgan, Łukasiewicz, Hilbert, Peirce, Post, Hintikka, Bolzano, and others. When deciding whether to use this for your course, beside the considerations already mentioned, another along which this fares favorably is price. At $59, it is a chunk cheaper than Mendelson ($85) and Enderton ($102), even if the former is paperback and the latter two hardcover. With the authors’ teaching experience behind them, their offering is well worth considering for your introductory, undergraduate logic course. Robert Lubarsky Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA. Robert.Lubarsky@alum.mit.edu.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"267 - 268"},"PeriodicalIF":0.6,"publicationDate":"2008-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S107989860000175X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57303088","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}

{"title":"Hyperlinear and Sofic Groups: A Brief Guide","authors":"V. Pestov","doi":"10.2178/bsl/1231081461","DOIUrl":"https://doi.org/10.2178/bsl/1231081461","url":null,"abstract":"Abstract This is an introductory survey of the emerging theory of two new classes of (discrete, countable) groups, called hyperlinear and sofic groups. They can be characterized as subgroups of metric ultraproducts of families of, respectively, unitary groups U(n) and symmetric groups Sn , n ∈ ℕ. Hyperlinear groups come from theory of operator algebras (Connes' Embedding Problem), while sofic groups, introduced by Gromov, are motivated by a problem of symbolic dynamics (Gottschalk's Surjunctivity Conjecture). Open questions are numerous, in particular it is still unknown if every group is hyperlinear and/or sofic.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"449 - 480"},"PeriodicalIF":0.6,"publicationDate":"2008-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2178/bsl/1231081461","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68346720","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}

{"title":"Cherlin Gregory and Hrushovski Ehud . Finite structures with few types . Annals of Mathematics Studies. Princeton University Press, 2003, vi + 196 pp.","authors":"Vera Koponen","doi":"10.2178/bsl/1208358847","DOIUrl":"https://doi.org/10.2178/bsl/1208358847","url":null,"abstract":"Gregory Cherlin and Ehud Hrushovski. Finite structures with few types. Annals of Mathematics Studies. Princeton University Press, 2003, vi + 196pp.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"114 - 116"},"PeriodicalIF":0.6,"publicationDate":"2008-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2178/bsl/1208358847","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68346110","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}

{"title":"Graham Priest. Towards non-being: the logic and metaphysics of intentionality. Oxford University Press, 2005, xi + 190 pp.","authors":"Thomas Hofweber","doi":"10.1017/S1079898600001864","DOIUrl":"https://doi.org/10.1017/S1079898600001864","url":null,"abstract":"type-amalgamation property in the book. The model theoretic analysis also shows that the class of structures which have a smoothly approximable expansion can be characterized as the class of structures which satisfies nine model theoretic properties, a few of which have just been mentioned. Many of the results presented depend on weaker assumptions than smooth approximability, such as א0-categoricity and finite rank. As shown in [Kantor, Liebeck, Macpherson, op. cit.], every smoothly approximable structure M has the following property, called pseudofiniteness: If φ is a sentence which is true in M then φ is true in a finite substructure of M . It follows that the complete theory of a smoothly approximable structure is not finitely axiomatizable. By developing further the method of envelopes and techniques of G. Ahlbrandt and M. Ziegler (used for strongly minimal totally categorical theories) it is shown that the complete theory of any smoothly approximable structure is quasifinitely axiomatizable, meaning that the theory is axiomatized by a finite number of axiom schemes. This extends earlier results about pseudofiniteness and quasifinite axiomatizability for א0-categorical א0-stable theories. In the last chapter, which builds on methods used for quasifinite axiomatizability, decidability problems are considered. For instance, given a language with a finite signature containing only relation symbols and a sentence in this language, it is decidable whether the sentence has a stable homogeneous model. Also, in a language with finite signature, one can decide whether a sentence has a finite model with a given number of 4-types. For some results the classification of finite simple groups is used and a discussion of this is given at the end of the book. The book is technically difficult, proofs are often quite compressed and it expects that the reader is familiar with various notions from model theory and algebra; so the book demands plenty of the reader. An error (the statement of Lemma 2.4.8) is corrected in [G. Cherlin, M. Djordjević, E. Hrushovski, The Journal of Symbolic Logic, vol. 70 (2005), pp. 1359–1364]. Vera Koponen Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden. vera@math.uu.se.","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"128 1","pages":"116 - 118"},"PeriodicalIF":0.6,"publicationDate":"2008-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S1079898600001864","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57303281","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}

{"title":"Mohammad Ardeshir. Manteghé Riazi (Mathematical Logic) . Hermes Publications, Tehran, 2005, 262 pp.","authors":"A. Enayat","doi":"10.1017/S1079898600001876","DOIUrl":"https://doi.org/10.1017/S1079898600001876","url":null,"abstract":"","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"118 - 119"},"PeriodicalIF":0.6,"publicationDate":"2008-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S1079898600001876","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57303514","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}

{"title":"BSL volume 14 issue 1 Cover and Front matter","authors":"","doi":"10.1017/s1079898600009628","DOIUrl":"https://doi.org/10.1017/s1079898600009628","url":null,"abstract":"","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"f1 - f6"},"PeriodicalIF":0.6,"publicationDate":"2008-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/s1079898600009628","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57315737","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}

{"title":"2007 European Summer Meeting of the Association for Symbolic Logic: Logic Colloquium '07","authors":"S. Lempp","doi":"10.2178/bsl/1208358849","DOIUrl":"https://doi.org/10.2178/bsl/1208358849","url":null,"abstract":"s of invited and contributed talks given in person or by title by members of the Association follow. For the Program Committee Steffen Lempp Abstracts of invited joint ASL–LICS hour lecturess of invited joint ASL–LICS hour lectures MARTIN HYLAND, Combinatorics of proofs. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, DPMMS, CMS, Wilberforce Road, Cambridge CB3 0WB, UK. E-mail: m.hyland@dpmms.cam.ac.uk. Ideally interpretations of proofs should exhibit some essential combinatorial features in an interesting and appealing way. As a case study, one can consider the notion of innocent strategy which is the basis for a game semantical interpretation of proofs and programmes. Some combinatorial content of this notion is sketched in the joint LICS paper accompanying this talk, whose abstract reads as follows. We show how to construct the category of games and innocent strategies from a more primitive category of games. On that category we define a comonad and monad with the former distributing over the latter. Innocent strategies are the maps in the induced two-sided Kleisli category. Thus the problematic composition of innocent strategies reflects the use of the distributive law. The composition of simple strategies, and the combinatorics of pointers used to give the comonad and monad are themselves described in categorical terms. The notions of view and of legal play arise naturally in the explanation of the distributivity. The category-theoretic perspective provides a clear discipline for the necessary combinatorics. There are other instances of a kind of categorical combinatorics of proofs, but in this talk I shall restrict myself to the one instance. COLIN STIRLING, Higher-order matching, games and automata. School of Informatics, University of Edinburgh, The King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK. E-mail: cps@inf.ed.ac.uk. We describe a particular case wheremethods such asmodel-checking as used in verification are transferred to simply typed lambda calculus. Higher-order matching is the problem given t = u where t, u are terms of simply typed lambda-calculus and u is closed, is there a substitution S such that tS and u have the same normal formwith respect to beta eta-equality: can t be pattern matched to u? In the talk we consider the question: can we characterize the set of all solution terms to a matching problem? We provide an automata-theoretic account that is relative to resource: given a matching problem and a finite set of variables and constants, the (possibly infinite) set of terms that are built from those components and that solve the problem is regular. The characterization uses standard bottom-up tree automata. However, the technical proof uses a game-theoretic characterization of matching. LOGIC COLLOQUIUM ’07 125 Abstracts of invited joint ASL–LICS thirty-minute lecturess of invited joint ASL–LICS thirty-minute lectures CRISTIANO CALCAGNO, Can logic tame systems programs? Dept. o","PeriodicalId":55307,"journal":{"name":"Bulletin of Symbolic Logic","volume":"14 1","pages":"123 - 159"},"PeriodicalIF":0.6,"publicationDate":"2008-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2178/bsl/1208358849","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68345910","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}